Abstract. In this work it is shown that there are some spatially homogeneous but anisotropic mode... more Abstract. In this work it is shown that there are some spatially homogeneous but anisotropic models (Kantowski-Sachs and Bianchi type-III), with a positive cosmological constant, for which the inhomogeneities in the distribution of matter on the surface of the last scattering produce anisotropies (in large angular scales ϑ ∼> 10◦) that do not differ from the ones produced in Friedmann-Lemâıtre-Robertson-Walker (FLRW) models, if the density parameters are finely tuned. Namely, for adiabatic initial conditions, the Sachs-Wolfe effect in these anisotropic models is equal to the one obtained for isotropic models: δTT = 1
In this work it is shown for some spatially homogeneous but anisotropic models how the inhomogene... more In this work it is shown for some spatially homogeneous but anisotropic models how the inhomogeneities in the distribution of matter on the surface of the last scattering produce anisotropies in large angular scales (larger than ϑ ∼ > 2 •) which do not differ from the ones produced in Friedmann-Lemaître-Robertson-Walker (FLRW) geometries. That is, for these anisotropic models, the imprint left on the cosmic microwave background radiation (CMBR) by the primordial density fluctuations, in the form of a fractional variation of the temperature of this radiation, is governed by the same expression as the one given for FLRW models. More precisely, under adiabatic initial conditions, the classical Sachs-Wolfe effect is recovered, provided the anisotropy of the overall expansion is small. This conclusion is in agreement with previous work on the same anisotropic models where we found that they may go through an 'isotropization' process up to the point that the observations are unable to distinguish them from the standard FLRW model, if the Hubble parameters along the orthogonal directions are assumed to be approximately equal at the present epoch. Here we assumed upper bounds on the present values of anisotropic parameters imposed by COBE observations.
Os enigmas da expansão do Universo: discussão e análise dos conceitos e preconceitos de uma grande descoberta
A expansão do Universo é uma das maiores descobertas do século XX. É talvez o facto mais relevant... more A expansão do Universo é uma das maiores descobertas do século XX. É talvez o facto mais relevante descoberto pelo homem acerca das suas origens. Por outro lado, até à identicação da radiação cósmica de fundo no domínio das micro-ondas, por Arnio Penzias e Robert Wilson em 1965, o reconhecimento de que a recessão das galáxias distantes aumenta com a distância foi a observação astronómica que mais estimulou o nascimento da cosmologia moderna. Este resultado observacional esta sobretudo associado ao astrónomo americano Edwin Hubble (1889-1953), que por essa razão é frequentemente identicado como o astrónomo que descobriu a expansão do Universo, na medida em que a descoberta da recessão das galáxias distantes foi entendida como uma prova da expansão do Universo. Neste contexto, é o seu artigo de 1929 que é habitualmente citado sempre que a expansão do Universo e atribuída a Hubble. Contudo, em nenhuma dessas páginas Hubble alguma vez se refere à expansão do Universo. Veremos, aliás, que o processo que conduz a este resultado é um caminho longo e complexo, no qual intervieram vários astrónomos e físicos teóricos, e cuja interpretação é ainda hoje alvo de debates acalorados. Vamos aqui recordar alguns dos autores e respectivos trabalhos que mais contribuíram para a ideia da expansão do Universo, bem como analisar alguns dos seus pressupostos. Discutiremos depois a possibilidade de existirem variantes do modelo padrão compatíveis com as observações actuais, tendo em conta a existência provável de heterogeneidades na distribuição da matéria numa época muito primitiva da História do Universo.
Following the recent recognition of a positive value for the vacuum energy density and the realiz... more Following the recent recognition of a positive value for the vacuum energy density and the realization that a simple Kantowski-Sachs model might fit the classical tests of cosmology, we study the qualitative behavior of three anisotropic and homogeneous models: Kantowski-Sachs, Bianchi type-I and Bianchi type-III universes, with dust and a cosmological constant, in order to find out which are physically permitted. We find that these models undergo isotropization up to the point that the observations will not be able to distinguish between them and the standard model, except for the Kantowski-Sachs model (Ω k 0 < 0) and for the Bianchi type-III (Ω k 0 > 0) with Ω Λ 0 smaller than some critical value Ω Λ M. Even if one imposes that the Universe should be nearly isotropic since the last scattering epoch (z ≈ 1000), meaning that the Universe should have approximately the same Hubble parameter in all directions (considering the COBE 4-Year data), there is still a large range for the matter density parameter compatible with Kantowsky-Sachs and Bianchi type-III if |Ω 0 + Ω Λ 0 − 1| ≤ δ, for a very small δ. The Bianchi type-I model becomes exactly isotropic owing to our restrictions and we have Ω 0 + Ω Λ 0 = 1 in this case. Of course, all these models approach locally an exponential expanding state provided the cosmological constant Ω Λ > Ω Λ M .
Dust-filled axially symmetric universes with a cosmological constant. Paulo Aguiar * and Paulo Cr... more Dust-filled axially symmetric universes with a cosmological constant. Paulo Aguiar * and Paulo Crawford Centro de Física Nuclear e Departamento de Física, da Faculdade de Ciênicas, da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal. ...
In this paper we show that the cosmological standard models can describe our universe very realis... more In this paper we show that the cosmological standard models can describe our universe very realistic way if we add a positive value of the cosmological constant, without the need for the introduction of cold dark matter. Also we clarify that it is physically allowed objects to move in the Universe at speeds greater than light speed without violation of Einstein's postulates.
Universal Journal of Physics and Application, 2016
Following the recognition of a positive value for the vacuum energy density and the realization t... more Following the recognition of a positive value for the vacuum energy density and the realization that a simple Kantowski-Sachs model might fit the classical tests of cosmology, we study the qualitative behavior of three anisotropic and homogeneous models: Kantowski-Sachs, Bianchi type-I and Bianchi type-III universes, with dust and a cosmological constant, in order to find out which are physically permitted. We find that these models undergo isotropization up to the point that the observations will not be able to distinguish between them and the standard model, except for the Kantowski-Sachs model (Ω k0 < 0) and for the Bianchi type-III (Ω k0 > 0) with Ω Λ0 smaller than some critical value Ω ΛM. Even if one imposes that the Universe should be nearly isotropic since the last scattering epoch (z ≈ 1000), meaning that the Universe should have approximately the same Hubble parameter in all directions (considering the COBE 4-Year data), there is still a large range for the matter density parameter compatible with Kantowsky-Sachs and Bianchi type-III if |Ω 0 + Ω Λ0 − 1| ≤ δ, for a very small δ. The Bianchi type-I model becomes exactly isotropic owing to our restrictions and we have Ω 0 + Ω Λ0 = 1 in this case. Of course, all these models approach locally an exponential expanding state provided the cosmological constant Ω Λ > Ω ΛM .
A expansão do Universo é uma das maiores descobertas
do século XX. É talvez o facto mais relevant... more A expansão do Universo é uma das maiores descobertas do século XX. É talvez o facto mais relevante descoberto pelo homem acerca das suas origens. Por outro lado, até à identicação da radiação cósmica de fundo no domínio das micro-ondas, por Arnio Penzias e Robert Wilson em 1965, o reconhecimento de que a recessão das galáxias distantes aumenta com a distância foi a observação astronómica que mais estimulou o nascimento da cosmologia moderna. Este resultado observacional esta sobretudo associado ao astrónomo americano Edwin Hubble (1889-1953), que por essa razão é frequentemente identicado como o astrónomo que descobriu a expansão do Universo, na medida em que a descoberta da recessão das galáxias distantes foi entendida como uma prova da expansão do Universo. Neste contexto, é o seu artigo de 1929 que é habitualmente citado sempre que a expansão do Universo e atribuída a Hubble. Contudo, em nenhuma dessas páginas Hubble alguma vez se refere à expansão do Universo. Veremos, aliás, que o processo que conduz a este resultado é um caminho longo e complexo, no qual intervieram vários astrónomos e físicos teóricos, e cuja interpretação é ainda hoje alvo de debates acalorados. Vamos aqui recordar alguns dos autores e respectivos trabalhos que mais contribuíram para a ideia da expansão do Universo, bem como analisar alguns dos seus pressupostos. Discutiremos depois a possibilidade de existirem variantes do modelo padrão compatíveis com as observações actuais, tendo em conta a existência provável de heterogeneidades na distribuição da matéria numa época muito primitiva da História do Universo.
In this work it is shown for some spatially homogeneous but anisotropic models how the inhomogene... more In this work it is shown for some spatially homogeneous but anisotropic models how the inhomogeneities in the distribution of matter on the surface of the last scattering produce anisotropies in large angular scales (larger than $\vartheta \gtrsim 2^\circ$) which do not differ from the ones produced in Friedmann-Lema\^itre-Robertson-Walker (FLRW) geometries. That is, for these anisotropic models, the imprint left on the cosmic microwave background radiation (CMBR) by the primordial density fluctuations, in the form of a fractional variation of the temperature of this radiation, is governed by the same expression as the one given for FLRW models. More precisely, under adiabatic initial conditions, the classical Sachs-Wolfe effect is recovered, provided the anisotropy of the overall expansion is small. This conclusion is in agreement with previous work on the same anisotropic models where we found that they may go through an `isotropization' process up to the point that the observations are unable to distinguish them from the standard FLRW model, if the Hubble parameters along the orthogonal directions are assumed to be approximately equal at the present epoch. Here we assumed upper bounds on the present values of anisotropic parameters imposed by COBE observations.
Following the recent recognition of a positive value for the vacuum energy density and the realiz... more Following the recent recognition of a positive value for the vacuum energy density and the realization that a simple Kantowski-Sachs model might fit classical tests of cosmology, we study the qualitative behavior of three anisotropic and homogeneous models, Kantowski-Sachs, Bianchi type-I and Bianchi type-III universes, with dust and a cosmological constant, in order to find out which are physically permitted. We find that these models undergo isotropization up to the point that the observations will not be able to distinguish between them and the standard model, except for the Kantowski-Sachs model (Ωk0<0) and for the Bianchi type-III model (Ωk0>0) with ΩΛ0 smaller than some critical value ΩΛM. Even if one imposes that the Universe should be nearly isotropic since the last scattering epoch (z~1000), meaning that the Universe should have approximately the same Hubble parameter in all directions (considering the COBE 4-year data), there is still a large range for the matter density parameter compatible with Kantowski-Sachs and Bianchi type-III models if \|Ω0+ΩΛ0-1\|<=δ, for a very small δ. The Bianchi type-I model becomes exactly isotropic owing to our restrictions and we have Ω0+ΩΛ0=1 in this case. Of course, all these models approach locally an exponential expanding state provided the cosmological constant ΩΛ>ΩΛM.
Following the recent recognition of a positive value for the vacuum energy density and the realiz... more Following the recent recognition of a positive value for the vacuum energy density and the realization that a simple Kantowski-Sachs model might fit the classical tests of cosmology, we study the qualitative behavior of three anisotropic and homogeneous models: Kantowski-Sachs, Bianchi type-I and Bianchi type-III universes, with dust and a cosmological constant, in order to find out which are physically permitted. We find that these models undergo isotropization up to the point that the observations will not be able to distinguish between them and the standard model, except for the Kantowski-Sachs model $(\Omega_{k_{0}}<0)$ and for the Bianchi type-III $(\Omega_{k_{0}}>0)$ with $\Omega_{\Lambda_{0}}$ smaller than some critical value $\Omega_{\Lambda_{M}}$. Even if one imposes that the Universe should be nearly isotropic since the last scattering epoch ($z\approx 1000$), meaning that the Universe should have approximately the same Hubble parameter in all directions (considering the COBE 4-Year data), there is still a large range for the matter density parameter compatible with Kantowsky-Sachs and Bianchi type-III if $|\Omega_0+\Omega_{\Lambda_0}-1|\leq \delta$, for a very small $\delta$ . The Bianchi type-I model becomes exactly isotropic owing to our restrictions and we have $\Omega_0+\Omega_{\Lambda_0}=1$ in this case. Of course, all these models approach locally an exponential expanding state provided the cosmological constant $\Omega_\Lambda>\Omega_{\Lambda_{M}}$.
In this work it is shown for some spatially homogeneous but anisotropic models how the inhomogene... more In this work it is shown for some spatially homogeneous but anisotropic models how the inhomogeneities in the distribution of matter on the surface of the last scattering produce anisotropies in large angular scales (larger than $\vartheta \gtrsim 2^\circ$) which do not differ from the ones produced in Friedmann-Lema\^itre-Robertson-Walker (FLRW) geometries. That is, for these anisotropic models, the imprint left on the cosmic microwave background radiation (CMBR) by the primordial density fluctuations, in the form of a fractional variation of the temperature of this radiation, is governed by the same expression as the one given for FLRW models. More precisely, under adiabatic initial conditions, the classical Sachs-Wolfe effect is recovered, provided the anisotropy of the overall expansion is small. This conclusion is in agreement with previous work on the same anisotropic models where we found that they may go through an `isotropization' process up to the point that the observations are unable to distinguish them from the standard FLRW model, if the Hubble parameters along the orthogonal directions are assumed to be approximately equal at the present epoch. Here we assumed upper bounds on the present values of anisotropic parameters imposed by COBE observations.
Following the recent recognition of a positive value for the vacuum energy density and the realiz... more Following the recent recognition of a positive value for the vacuum energy density and the realization that a simple Kantowski-Sachs model might fit classical tests of cosmology, we study the qualitative behavior of three anisotropic and homogeneous models, Kantowski-Sachs, Bianchi type-I and Bianchi type-III universes, with dust and a cosmological constant, in order to find out which are physically permitted. We find that these models undergo isotropization up to the point that the observations will not be able to distinguish between them and the standard model, except for the Kantowski-Sachs model (Ωk0<0) and for the Bianchi type-III model (Ωk0>0) with ΩΛ0 smaller than some critical value ΩΛM. Even if one imposes that the Universe should be nearly isotropic since the last scattering epoch (z~1000), meaning that the Universe should have approximately the same Hubble parameter in all directions (considering the COBE 4-year data), there is still a large range for the matter density parameter compatible with Kantowski-Sachs and Bianchi type-III models if \|Ω0+ΩΛ0-1\|<=δ, for a very small δ. The Bianchi type-I model becomes exactly isotropic owing to our restrictions and we have Ω0+ΩΛ0=1 in this case. Of course, all these models approach locally an exponential expanding state provided the cosmological constant ΩΛ>ΩΛM.
Abstract. In this work it is shown that there are some spatially homogeneous but anisotropic mode... more Abstract. In this work it is shown that there are some spatially homogeneous but anisotropic models (Kantowski-Sachs and Bianchi type-III), with a positive cosmological constant, for which the inhomogeneities in the distribution of matter on the surface of the last scattering produce anisotropies (in large angular scales ϑ ∼> 10◦) that do not differ from the ones produced in Friedmann-Lemâıtre-Robertson-Walker (FLRW) models, if the density parameters are finely tuned. Namely, for adiabatic initial conditions, the Sachs-Wolfe effect in these anisotropic models is equal to the one obtained for isotropic models: δTT = 1
In this work it is shown for some spatially homogeneous but anisotropic models how the inhomogene... more In this work it is shown for some spatially homogeneous but anisotropic models how the inhomogeneities in the distribution of matter on the surface of the last scattering produce anisotropies in large angular scales (larger than ϑ ∼ > 2 •) which do not differ from the ones produced in Friedmann-Lemaître-Robertson-Walker (FLRW) geometries. That is, for these anisotropic models, the imprint left on the cosmic microwave background radiation (CMBR) by the primordial density fluctuations, in the form of a fractional variation of the temperature of this radiation, is governed by the same expression as the one given for FLRW models. More precisely, under adiabatic initial conditions, the classical Sachs-Wolfe effect is recovered, provided the anisotropy of the overall expansion is small. This conclusion is in agreement with previous work on the same anisotropic models where we found that they may go through an 'isotropization' process up to the point that the observations are unable to distinguish them from the standard FLRW model, if the Hubble parameters along the orthogonal directions are assumed to be approximately equal at the present epoch. Here we assumed upper bounds on the present values of anisotropic parameters imposed by COBE observations.
Os enigmas da expansão do Universo: discussão e análise dos conceitos e preconceitos de uma grande descoberta
A expansão do Universo é uma das maiores descobertas do século XX. É talvez o facto mais relevant... more A expansão do Universo é uma das maiores descobertas do século XX. É talvez o facto mais relevante descoberto pelo homem acerca das suas origens. Por outro lado, até à identicação da radiação cósmica de fundo no domínio das micro-ondas, por Arnio Penzias e Robert Wilson em 1965, o reconhecimento de que a recessão das galáxias distantes aumenta com a distância foi a observação astronómica que mais estimulou o nascimento da cosmologia moderna. Este resultado observacional esta sobretudo associado ao astrónomo americano Edwin Hubble (1889-1953), que por essa razão é frequentemente identicado como o astrónomo que descobriu a expansão do Universo, na medida em que a descoberta da recessão das galáxias distantes foi entendida como uma prova da expansão do Universo. Neste contexto, é o seu artigo de 1929 que é habitualmente citado sempre que a expansão do Universo e atribuída a Hubble. Contudo, em nenhuma dessas páginas Hubble alguma vez se refere à expansão do Universo. Veremos, aliás, que o processo que conduz a este resultado é um caminho longo e complexo, no qual intervieram vários astrónomos e físicos teóricos, e cuja interpretação é ainda hoje alvo de debates acalorados. Vamos aqui recordar alguns dos autores e respectivos trabalhos que mais contribuíram para a ideia da expansão do Universo, bem como analisar alguns dos seus pressupostos. Discutiremos depois a possibilidade de existirem variantes do modelo padrão compatíveis com as observações actuais, tendo em conta a existência provável de heterogeneidades na distribuição da matéria numa época muito primitiva da História do Universo.
Following the recent recognition of a positive value for the vacuum energy density and the realiz... more Following the recent recognition of a positive value for the vacuum energy density and the realization that a simple Kantowski-Sachs model might fit the classical tests of cosmology, we study the qualitative behavior of three anisotropic and homogeneous models: Kantowski-Sachs, Bianchi type-I and Bianchi type-III universes, with dust and a cosmological constant, in order to find out which are physically permitted. We find that these models undergo isotropization up to the point that the observations will not be able to distinguish between them and the standard model, except for the Kantowski-Sachs model (Ω k 0 < 0) and for the Bianchi type-III (Ω k 0 > 0) with Ω Λ 0 smaller than some critical value Ω Λ M. Even if one imposes that the Universe should be nearly isotropic since the last scattering epoch (z ≈ 1000), meaning that the Universe should have approximately the same Hubble parameter in all directions (considering the COBE 4-Year data), there is still a large range for the matter density parameter compatible with Kantowsky-Sachs and Bianchi type-III if |Ω 0 + Ω Λ 0 − 1| ≤ δ, for a very small δ. The Bianchi type-I model becomes exactly isotropic owing to our restrictions and we have Ω 0 + Ω Λ 0 = 1 in this case. Of course, all these models approach locally an exponential expanding state provided the cosmological constant Ω Λ > Ω Λ M .
Dust-filled axially symmetric universes with a cosmological constant. Paulo Aguiar * and Paulo Cr... more Dust-filled axially symmetric universes with a cosmological constant. Paulo Aguiar * and Paulo Crawford Centro de Física Nuclear e Departamento de Física, da Faculdade de Ciênicas, da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal. ...
In this paper we show that the cosmological standard models can describe our universe very realis... more In this paper we show that the cosmological standard models can describe our universe very realistic way if we add a positive value of the cosmological constant, without the need for the introduction of cold dark matter. Also we clarify that it is physically allowed objects to move in the Universe at speeds greater than light speed without violation of Einstein's postulates.
Universal Journal of Physics and Application, 2016
Following the recognition of a positive value for the vacuum energy density and the realization t... more Following the recognition of a positive value for the vacuum energy density and the realization that a simple Kantowski-Sachs model might fit the classical tests of cosmology, we study the qualitative behavior of three anisotropic and homogeneous models: Kantowski-Sachs, Bianchi type-I and Bianchi type-III universes, with dust and a cosmological constant, in order to find out which are physically permitted. We find that these models undergo isotropization up to the point that the observations will not be able to distinguish between them and the standard model, except for the Kantowski-Sachs model (Ω k0 < 0) and for the Bianchi type-III (Ω k0 > 0) with Ω Λ0 smaller than some critical value Ω ΛM. Even if one imposes that the Universe should be nearly isotropic since the last scattering epoch (z ≈ 1000), meaning that the Universe should have approximately the same Hubble parameter in all directions (considering the COBE 4-Year data), there is still a large range for the matter density parameter compatible with Kantowsky-Sachs and Bianchi type-III if |Ω 0 + Ω Λ0 − 1| ≤ δ, for a very small δ. The Bianchi type-I model becomes exactly isotropic owing to our restrictions and we have Ω 0 + Ω Λ0 = 1 in this case. Of course, all these models approach locally an exponential expanding state provided the cosmological constant Ω Λ > Ω ΛM .
A expansão do Universo é uma das maiores descobertas
do século XX. É talvez o facto mais relevant... more A expansão do Universo é uma das maiores descobertas do século XX. É talvez o facto mais relevante descoberto pelo homem acerca das suas origens. Por outro lado, até à identicação da radiação cósmica de fundo no domínio das micro-ondas, por Arnio Penzias e Robert Wilson em 1965, o reconhecimento de que a recessão das galáxias distantes aumenta com a distância foi a observação astronómica que mais estimulou o nascimento da cosmologia moderna. Este resultado observacional esta sobretudo associado ao astrónomo americano Edwin Hubble (1889-1953), que por essa razão é frequentemente identicado como o astrónomo que descobriu a expansão do Universo, na medida em que a descoberta da recessão das galáxias distantes foi entendida como uma prova da expansão do Universo. Neste contexto, é o seu artigo de 1929 que é habitualmente citado sempre que a expansão do Universo e atribuída a Hubble. Contudo, em nenhuma dessas páginas Hubble alguma vez se refere à expansão do Universo. Veremos, aliás, que o processo que conduz a este resultado é um caminho longo e complexo, no qual intervieram vários astrónomos e físicos teóricos, e cuja interpretação é ainda hoje alvo de debates acalorados. Vamos aqui recordar alguns dos autores e respectivos trabalhos que mais contribuíram para a ideia da expansão do Universo, bem como analisar alguns dos seus pressupostos. Discutiremos depois a possibilidade de existirem variantes do modelo padrão compatíveis com as observações actuais, tendo em conta a existência provável de heterogeneidades na distribuição da matéria numa época muito primitiva da História do Universo.
In this work it is shown for some spatially homogeneous but anisotropic models how the inhomogene... more In this work it is shown for some spatially homogeneous but anisotropic models how the inhomogeneities in the distribution of matter on the surface of the last scattering produce anisotropies in large angular scales (larger than $\vartheta \gtrsim 2^\circ$) which do not differ from the ones produced in Friedmann-Lema\^itre-Robertson-Walker (FLRW) geometries. That is, for these anisotropic models, the imprint left on the cosmic microwave background radiation (CMBR) by the primordial density fluctuations, in the form of a fractional variation of the temperature of this radiation, is governed by the same expression as the one given for FLRW models. More precisely, under adiabatic initial conditions, the classical Sachs-Wolfe effect is recovered, provided the anisotropy of the overall expansion is small. This conclusion is in agreement with previous work on the same anisotropic models where we found that they may go through an `isotropization' process up to the point that the observations are unable to distinguish them from the standard FLRW model, if the Hubble parameters along the orthogonal directions are assumed to be approximately equal at the present epoch. Here we assumed upper bounds on the present values of anisotropic parameters imposed by COBE observations.
Following the recent recognition of a positive value for the vacuum energy density and the realiz... more Following the recent recognition of a positive value for the vacuum energy density and the realization that a simple Kantowski-Sachs model might fit classical tests of cosmology, we study the qualitative behavior of three anisotropic and homogeneous models, Kantowski-Sachs, Bianchi type-I and Bianchi type-III universes, with dust and a cosmological constant, in order to find out which are physically permitted. We find that these models undergo isotropization up to the point that the observations will not be able to distinguish between them and the standard model, except for the Kantowski-Sachs model (Ωk0<0) and for the Bianchi type-III model (Ωk0>0) with ΩΛ0 smaller than some critical value ΩΛM. Even if one imposes that the Universe should be nearly isotropic since the last scattering epoch (z~1000), meaning that the Universe should have approximately the same Hubble parameter in all directions (considering the COBE 4-year data), there is still a large range for the matter density parameter compatible with Kantowski-Sachs and Bianchi type-III models if \|Ω0+ΩΛ0-1\|<=δ, for a very small δ. The Bianchi type-I model becomes exactly isotropic owing to our restrictions and we have Ω0+ΩΛ0=1 in this case. Of course, all these models approach locally an exponential expanding state provided the cosmological constant ΩΛ>ΩΛM.
Following the recent recognition of a positive value for the vacuum energy density and the realiz... more Following the recent recognition of a positive value for the vacuum energy density and the realization that a simple Kantowski-Sachs model might fit the classical tests of cosmology, we study the qualitative behavior of three anisotropic and homogeneous models: Kantowski-Sachs, Bianchi type-I and Bianchi type-III universes, with dust and a cosmological constant, in order to find out which are physically permitted. We find that these models undergo isotropization up to the point that the observations will not be able to distinguish between them and the standard model, except for the Kantowski-Sachs model $(\Omega_{k_{0}}<0)$ and for the Bianchi type-III $(\Omega_{k_{0}}>0)$ with $\Omega_{\Lambda_{0}}$ smaller than some critical value $\Omega_{\Lambda_{M}}$. Even if one imposes that the Universe should be nearly isotropic since the last scattering epoch ($z\approx 1000$), meaning that the Universe should have approximately the same Hubble parameter in all directions (considering the COBE 4-Year data), there is still a large range for the matter density parameter compatible with Kantowsky-Sachs and Bianchi type-III if $|\Omega_0+\Omega_{\Lambda_0}-1|\leq \delta$, for a very small $\delta$ . The Bianchi type-I model becomes exactly isotropic owing to our restrictions and we have $\Omega_0+\Omega_{\Lambda_0}=1$ in this case. Of course, all these models approach locally an exponential expanding state provided the cosmological constant $\Omega_\Lambda>\Omega_{\Lambda_{M}}$.
In this work it is shown for some spatially homogeneous but anisotropic models how the inhomogene... more In this work it is shown for some spatially homogeneous but anisotropic models how the inhomogeneities in the distribution of matter on the surface of the last scattering produce anisotropies in large angular scales (larger than $\vartheta \gtrsim 2^\circ$) which do not differ from the ones produced in Friedmann-Lema\^itre-Robertson-Walker (FLRW) geometries. That is, for these anisotropic models, the imprint left on the cosmic microwave background radiation (CMBR) by the primordial density fluctuations, in the form of a fractional variation of the temperature of this radiation, is governed by the same expression as the one given for FLRW models. More precisely, under adiabatic initial conditions, the classical Sachs-Wolfe effect is recovered, provided the anisotropy of the overall expansion is small. This conclusion is in agreement with previous work on the same anisotropic models where we found that they may go through an `isotropization' process up to the point that the observations are unable to distinguish them from the standard FLRW model, if the Hubble parameters along the orthogonal directions are assumed to be approximately equal at the present epoch. Here we assumed upper bounds on the present values of anisotropic parameters imposed by COBE observations.
Following the recent recognition of a positive value for the vacuum energy density and the realiz... more Following the recent recognition of a positive value for the vacuum energy density and the realization that a simple Kantowski-Sachs model might fit classical tests of cosmology, we study the qualitative behavior of three anisotropic and homogeneous models, Kantowski-Sachs, Bianchi type-I and Bianchi type-III universes, with dust and a cosmological constant, in order to find out which are physically permitted. We find that these models undergo isotropization up to the point that the observations will not be able to distinguish between them and the standard model, except for the Kantowski-Sachs model (Ωk0<0) and for the Bianchi type-III model (Ωk0>0) with ΩΛ0 smaller than some critical value ΩΛM. Even if one imposes that the Universe should be nearly isotropic since the last scattering epoch (z~1000), meaning that the Universe should have approximately the same Hubble parameter in all directions (considering the COBE 4-year data), there is still a large range for the matter density parameter compatible with Kantowski-Sachs and Bianchi type-III models if \|Ω0+ΩΛ0-1\|<=δ, for a very small δ. The Bianchi type-I model becomes exactly isotropic owing to our restrictions and we have Ω0+ΩΛ0=1 in this case. Of course, all these models approach locally an exponential expanding state provided the cosmological constant ΩΛ>ΩΛM.
Uploads
Papers by Paulo Aguiar
do século XX. É talvez o facto mais relevante
descoberto pelo homem acerca das suas origens. Por
outro lado, até à identicação da radiação cósmica de
fundo no domínio das micro-ondas, por Arnio Penzias
e Robert Wilson em 1965, o reconhecimento de que a
recessão das galáxias distantes aumenta com a distância
foi a observação astronómica que mais estimulou
o nascimento da cosmologia moderna. Este resultado
observacional esta sobretudo associado ao astrónomo
americano Edwin Hubble (1889-1953), que por essa
razão é frequentemente identicado como o astrónomo
que descobriu a expansão do Universo, na medida em
que a descoberta da recessão das galáxias distantes foi
entendida como uma prova da expansão do Universo.
Neste contexto, é o seu artigo de 1929 que é habitualmente
citado sempre que a expansão do Universo
e atribuída a Hubble. Contudo, em nenhuma dessas
páginas Hubble alguma vez se refere à expansão do
Universo. Veremos, aliás, que o processo que conduz a
este resultado é um caminho longo e complexo, no qual
intervieram vários astrónomos e físicos teóricos, e cuja
interpretação é ainda hoje alvo de debates acalorados.
Vamos aqui recordar alguns dos autores e respectivos
trabalhos que mais contribuíram para a ideia da expansão
do Universo, bem como analisar alguns dos seus
pressupostos. Discutiremos depois a possibilidade de
existirem variantes do modelo padrão compatíveis com
as observações actuais, tendo em conta a existência
provável de heterogeneidades na distribuição da matéria
numa época muito primitiva da História do Universo.
do século XX. É talvez o facto mais relevante
descoberto pelo homem acerca das suas origens. Por
outro lado, até à identicação da radiação cósmica de
fundo no domínio das micro-ondas, por Arnio Penzias
e Robert Wilson em 1965, o reconhecimento de que a
recessão das galáxias distantes aumenta com a distância
foi a observação astronómica que mais estimulou
o nascimento da cosmologia moderna. Este resultado
observacional esta sobretudo associado ao astrónomo
americano Edwin Hubble (1889-1953), que por essa
razão é frequentemente identicado como o astrónomo
que descobriu a expansão do Universo, na medida em
que a descoberta da recessão das galáxias distantes foi
entendida como uma prova da expansão do Universo.
Neste contexto, é o seu artigo de 1929 que é habitualmente
citado sempre que a expansão do Universo
e atribuída a Hubble. Contudo, em nenhuma dessas
páginas Hubble alguma vez se refere à expansão do
Universo. Veremos, aliás, que o processo que conduz a
este resultado é um caminho longo e complexo, no qual
intervieram vários astrónomos e físicos teóricos, e cuja
interpretação é ainda hoje alvo de debates acalorados.
Vamos aqui recordar alguns dos autores e respectivos
trabalhos que mais contribuíram para a ideia da expansão
do Universo, bem como analisar alguns dos seus
pressupostos. Discutiremos depois a possibilidade de
existirem variantes do modelo padrão compatíveis com
as observações actuais, tendo em conta a existência
provável de heterogeneidades na distribuição da matéria
numa época muito primitiva da História do Universo.