A number of scalar field models proposed as alternatives to the standard inflationary scenario in... more A number of scalar field models proposed as alternatives to the standard inflationary scenario involve contracting phases which precede the universe's present phase of expansion. An important question concerning such models is whether there are effects which could potentially distinguish them from purely expanding cosmologies. Vector perturbations have recently been considered in this context. At first order such perturbations are not supported by a scalar field. In this paper, therefore, we consider second order vector perturbations. We show that such perturbations are generated by first order scalar mode-mode couplings, and give an explicit expression for them. We compare the magnitude of vector perturbations produced in collapsing models with the corresponding amplitudes produced during inflation, using a number of suitable power-law solutions to model the inflationary and collapsing scenarios. We conclude that the ratios of the magnitudes of these perturbations depend on the details of the collapsing scenario as well as on how the hot big bang is recovered, but for certain cases could be large, growing with the duration of the collapse.
With the help of families of density contrast indicators, we study the tendency of gravitational ... more With the help of families of density contrast indicators, we study the tendency of gravitational systems to become increasingly lumpy with time. Depending upon their domain of definition, these indicators could be local or global. We make a comparative study of these indicators in the context of inhomogeneous cosmological models of Lemaitre-Tolman and Szekeres. In particular, we look at the temporal asymptotic behaviour of these indicators and ask under what conditions, and for which class of models, they evolve monotonically in time. We find that for the case of ever-expanding models, there is a larger class of indicators that grow monotonically with time, whereas the corresponding class for the recollapsing models is more restricted. Nevertheless, in the absence of decaying modes, indicators exist which grow monotonically with time for both ever-expanding and recollapsing models simultaneously. On the other hand, no such indicators may found which grow monotonically if the decaying modes are allowed to exist. We also find the conditions for these indicators to be non-divergent at the initial singularity in both models. Our results can be of potential relevance for understanding structure formation in inhomogeneous settings and in debates regarding gravitational entropy and arrow of time. In particular, the spatial dependence of turning points in inhomogeneous cosmologies may result in multiple density contrast arrows in recollapsing models over certain epochs. We also find that different notions of asymptotic homogenisation may be deduced, depending upon the density contrast indicators used.
Planck data has not found the 'smoking gun' of non-Gaussianity that would have necessitated consi... more Planck data has not found the 'smoking gun' of non-Gaussianity that would have necessitated consideration of inflationary models beyond the simplest canonical single field scenarios. This raises the important question of what these results do imply for more general models, and in particular, multi-field inflation. In this paper we revisit four ways in which two-field scenarios can behave differently from single field models; two-field slow-roll dynamics, curvaton-type behaviour, inflation ending on an inhomogeneous hypersurface and modulated reheating. We study the constraints that Planck data puts on these classes of behaviour, focusing on the latter two which have been least studied in the recent literature. We show that these latter classes are almost equivalent, and extend their previous analyses by accounting for arbitrary evolution of the isocurvature mode which, in particular, places important limits on the Gaussian curvature of the reheating hypersurface. In general, however, we find that Planck bispectrum results only constrain certain regions of parameter space, leading us to conclude that inflation sourced by more than one scalar field remains an important possibility.
Anvar Shukurov and colleagues remember a theorist known for his work on stellar and galactic magn... more Anvar Shukurov and colleagues remember a theorist known for his work on stellar and galactic magnetism, who was also a prominent marine biologist.
We report our first results on comparing the variations of the solar internal rotation with solar... more We report our first results on comparing the variations of the solar internal rotation with solar activity, as predicted by non-linear solar dynamo modelling, with helioseismic measurements using the SOHO MDI data.
Abstract: The second of the annual BritGrav meetings on current research in Gravitational Physics... more Abstract: The second of the annual BritGrav meetings on current research in Gravitational Physics in Britain took place at the School of Mathematical Sciences of Queen Mary, University of London on June 10/11, 2002. 47 plenary talks of 12min duration were given. We make available the abstracts of the talks and the references to the electronic preprints at arXiv. org where they exist.
We briefly summarise and further discuss the observational implications of the model-independent ... more We briefly summarise and further discuss the observational implications of the model-independent scheme recently put forward by us for the reconstruction of dark energy. The scheme employs rather weak geometrical features of the luminosity-distance relation motivated by recent observations. Using the SNLS supernovae data, the reconstructed luminosity-distance curves best fitting the data are shown to favour a Universe with a varying dark energy density, expanding at a slower rate than the ΛCDM model. The ΛCDM model. however, cannot be ruled out at high significance levels, in line with other recent reconstructions. We highlight the degeneracy concerning the CDM density parameter Ωm 0 , which acts as a barrier against a conclusive determination of whether the dark agency is the cosmological constant.
arXiv: General Relativity and Quantum Cosmology, 2015
We argue against current proposals concerning the non-existence of time. We point out that a larg... more We argue against current proposals concerning the non-existence of time. We point out that a large number of these proposals rely, at least implicitly, on the assumption of `closure' (or `partial closure') of the laws of Physics. I.e. the assumption that laws of Physics as they are known today are either complete (and hence closed) or that they possess features that a hypothetical future `complete' theory must share (and hence are partially closed). Given that the assumption of closure of laws of Physics can never be verified operationally, it cannot justifiably be used to support the claim for non-existence of time. Some approaches against time are `timeless' at the primary level for the universe as a whole. In these approaches time arises at a secondary level, mostly in the sense of `time being abstracted from change'. On the other hand, there are other approaches that deny the existence of time altogether. We argue that metaphysical arguments of this type - si...
We explore some fundational issues regarding the splitting of D-dimensional EFE's w.r.t timel... more We explore some fundational issues regarding the splitting of D-dimensional EFE's w.r.t timelike and spacelike (D-1)-dimensional hypersurfaces, first without and then with thin matter sheets such as branes. We begin to implement methodology, that is well-established for the GR CP and IVP, in the new field of GR-based braneworlds, identifying and comparing many different choices of procedure. We abridge fragmentary parts of the literature of embeddings, putting the Campbell--Magaard theorem into context. We recollect and refine arguments why York and not elimination methods are used for the GR IVP. We compile a list of numerous mathematical and physical impasses to using timelike splits, whereas spacelike splits are known to be well-behaved. We however pursue both options to make contact with the current braneworld literature which is almost entirely based on timelike splits. We look at the Shiromizu-Maeda -Sasaki braneworld by means of reformulations which emphasize different as...
We study the dynamics of states perturbatively expanded about a harmonic system of loop quantum c... more We study the dynamics of states perturbatively expanded about a harmonic system of loop quantum cosmology, exhibiting a bounce. In particular, the evolution equations for the first and second order moments of the system are analyzed. These moments back-react on the trajectories of the expectation values of the state and hence alter the energy density at the bounce. This analysis is performed for isotropic loop quantum cosmology coupled to a scalar field with a small but non-zero constant potential, hence in a regime in which the kinetic energy of matter dominates. Analytic restrictions on the existence of dynamical coherent states and the meaning of semi-classicality within these systems are discussed. A numerical investigation of the trajectories of states that remain semi-classical across the bounce demonstrates that, at least for such states, the bounce persists and that its properties are similar to the standard case, in which the moments of the states are entirely neglected. However the bounce density does change, implying that a quantum bounce may not be guaranteed to happen when the potential is no longer negligible.
Global symmetries of the string effective action are employed to generate tilted, homogeneous Bia... more Global symmetries of the string effective action are employed to generate tilted, homogeneous Bianchi type VI h string cosmologies from a previously known stiff perfect fluid solution to Einstein gravity. The dilaton field is not constant on the surfaces of homogeneity. The future asymptotic state of the models is interpreted as a plane wave and is itself an exact solution to the string equations of motion to all orders in the inverse string tension. An inhomogeneous generalization of the Bianchi type III model is also found.
Positively-curved, oscillatory universes are studied within the context of Loop Quantum Cosmology... more Positively-curved, oscillatory universes are studied within the context of Loop Quantum Cosmology subject to a consistent semi-classical treatment. The semi-classical effects are reformulated in terms of an effective phantom fluid with a variable equation of state. In cosmologies sourced by a massless scalar field, these effects lead to a universe that undergoes ever-repeating cycles of expansion and contraction. The presence of a self-interaction potential for the field breaks the symmetry of the cycles and can enable the oscillations to establish the initial conditions for successful slow-roll inflation, even when the field is initially at the minimum of its potential with a small kinetic energy. The displacement of the field from its minimum is enhanced for lower and more natural values of the parameter that sets the effective quantum gravity scale. For sufficiently small values of this parameter, the universe can enter a stage of eternal self-reproduction.
In loop quantum gravity, modifications to the geometrical density cause a self-interacting scalar... more In loop quantum gravity, modifications to the geometrical density cause a self-interacting scalar field to accelerate away from a minimum of its potential. In principle, this mechanism can generate the conditions that subsequently lead to slow-roll inflation. The consequences for this mechanism of various quantization ambiguities arising within loop quantum cosmology are considered. For the case of a quadratic potential, it is found that some quantization procedures are more likely to generate a phase of slow-roll inflation. In general, however, loop quantum cosmology is robust to ambiguities in the quantization and extends the range of initial conditions for inflation.
We make a systematic study of the cosmological dynamics for a number of f (R) gravity theories in... more We make a systematic study of the cosmological dynamics for a number of f (R) gravity theories in Palatini formalism, using phase space analysis as well as numerical simulations. Considering homogeneous and isotropic models, we find a number of interesting results: (i) models based on theories of the type (a) f (R) = R − β/R n and (b) f (R) = R + αln R − β, unlike the metric formalism, are capable of producing the sequence of radiation-dominated, matter-dominated and de-Sitter periods, and (ii) models based on theories of the type (c) f (R) = R + αR m − β/R n can produce early as well as late accelerating phases but an early inflationary epoch does not seem to be compatible with the presence of a subsequent radiation-dominated era. Thus for the classes of models considered here, we have been unable to find the sequence of all four dynamical epochs required to account for the complete cosmological dynamics, even though three out of four phases are possible. We also place observational constraints on these models using the recently released supernovae data by the Supernova Legacy Survey as well as the baryon acoustic oscillation peak in the SDSS luminous red galaxy sample and the CMB shift parameter. The best-fit values are found to be n = 0.027, α = 4.63 for the models based on (a) and α = 0.11, β = 4.62 for the models based on (b), neither of which are significantly preferred over the ΛCDM model. Moreover, the logarithmic term alone is not capable of explaining the late acceleration. The models based on (c) are also consistent with the data with suitable choices of their parameters. We also find that some of the models for which the radiation-dominated epoch is absent prior to the matter-dominated era also fit the data. The reason for this apparent contradiction is that the combination of the data considered here does not place stringent enough constraints on the cosmological evolution prior to the decoupling epoch, which highlights the importance of our combined theoretical-observational approach to constrain models.
Families of anisotropic and inhomogeneous string cosmologies containing non-trivial dilaton and a... more Families of anisotropic and inhomogeneous string cosmologies containing non-trivial dilaton and axion fields are derived by applying the global symmetries of the string effective action to a generalized Einstein-Rosen metric. The models exhibit a twodimensional group of Abelian isometries. In particular, two classes of exact solutions are found that represent inhomogeneous generalizations of the Bianchi type VI h cosmology. The asymptotic behaviour of the solutions is investigated and further applications are briefly discussed.
We take a critical look at a recent conjecture concerning the past attractor in the pre-big-bang ... more We take a critical look at a recent conjecture concerning the past attractor in the pre-big-bang scenario. We argue that the Milne universe is unlikely to be a general past attractor for such models and support this with a number of examples.
Journal of Cosmology and Astroparticle Physics, 2005
The geodesics of a spacetime seldom coincide with those of an embedded submanifold of codimension... more The geodesics of a spacetime seldom coincide with those of an embedded submanifold of codimension one. We investigate this issue for higher-dimensional general relativity-like models, firstly in the simpler case without branes to isolate which features are already present, and then in the more complicated case with branes. The framework in which we consider branes is general enough to include asymmetric braneworlds but not thick branes. We apply our results on geodesics to study both the equivalence principle and cosmological singularities. Among the models we study these considerations favour Z 2 symmetric braneworlds with a negative bulk cosmological constant.
Journal of Cosmology and Astroparticle Physics, 2012
We calculate the conditions required to produce a large local trispectrum during two-field slow-r... more We calculate the conditions required to produce a large local trispectrum during two-field slow-roll inflation. This is done by extending and simplifying the 'heat-map' approach developed by Byrnes et al. The conditions required to generate a large trispectrum are broadly the same as those that can produce a large bispectrum. We derive a simple relation between τ NL and f NL for models with separable potentials, and furthermore show that g NL and τ NL can be related in specific circumstances. Additionally, we interpret the heatmaps dynamically, showing how they can be used as qualitative tools to understand the evolution of non-Gaussianity during inflation. We also show how f NL , τ NL and g NL are sourced by generic shapes in the inflationary potential, namely ridges, valleys and inflection points.
A number of scalar field models proposed as alternatives to the standard inflationary scenario in... more A number of scalar field models proposed as alternatives to the standard inflationary scenario involve contracting phases which precede the universe's present phase of expansion. An important question concerning such models is whether there are effects which could potentially distinguish them from purely expanding cosmologies. Vector perturbations have recently been considered in this context. At first order such perturbations are not supported by a scalar field. In this paper, therefore, we consider second order vector perturbations. We show that such perturbations are generated by first order scalar mode-mode couplings, and give an explicit expression for them. We compare the magnitude of vector perturbations produced in collapsing models with the corresponding amplitudes produced during inflation, using a number of suitable power-law solutions to model the inflationary and collapsing scenarios. We conclude that the ratios of the magnitudes of these perturbations depend on the details of the collapsing scenario as well as on how the hot big bang is recovered, but for certain cases could be large, growing with the duration of the collapse.
With the help of families of density contrast indicators, we study the tendency of gravitational ... more With the help of families of density contrast indicators, we study the tendency of gravitational systems to become increasingly lumpy with time. Depending upon their domain of definition, these indicators could be local or global. We make a comparative study of these indicators in the context of inhomogeneous cosmological models of Lemaitre-Tolman and Szekeres. In particular, we look at the temporal asymptotic behaviour of these indicators and ask under what conditions, and for which class of models, they evolve monotonically in time. We find that for the case of ever-expanding models, there is a larger class of indicators that grow monotonically with time, whereas the corresponding class for the recollapsing models is more restricted. Nevertheless, in the absence of decaying modes, indicators exist which grow monotonically with time for both ever-expanding and recollapsing models simultaneously. On the other hand, no such indicators may found which grow monotonically if the decaying modes are allowed to exist. We also find the conditions for these indicators to be non-divergent at the initial singularity in both models. Our results can be of potential relevance for understanding structure formation in inhomogeneous settings and in debates regarding gravitational entropy and arrow of time. In particular, the spatial dependence of turning points in inhomogeneous cosmologies may result in multiple density contrast arrows in recollapsing models over certain epochs. We also find that different notions of asymptotic homogenisation may be deduced, depending upon the density contrast indicators used.
Planck data has not found the 'smoking gun' of non-Gaussianity that would have necessitated consi... more Planck data has not found the 'smoking gun' of non-Gaussianity that would have necessitated consideration of inflationary models beyond the simplest canonical single field scenarios. This raises the important question of what these results do imply for more general models, and in particular, multi-field inflation. In this paper we revisit four ways in which two-field scenarios can behave differently from single field models; two-field slow-roll dynamics, curvaton-type behaviour, inflation ending on an inhomogeneous hypersurface and modulated reheating. We study the constraints that Planck data puts on these classes of behaviour, focusing on the latter two which have been least studied in the recent literature. We show that these latter classes are almost equivalent, and extend their previous analyses by accounting for arbitrary evolution of the isocurvature mode which, in particular, places important limits on the Gaussian curvature of the reheating hypersurface. In general, however, we find that Planck bispectrum results only constrain certain regions of parameter space, leading us to conclude that inflation sourced by more than one scalar field remains an important possibility.
Anvar Shukurov and colleagues remember a theorist known for his work on stellar and galactic magn... more Anvar Shukurov and colleagues remember a theorist known for his work on stellar and galactic magnetism, who was also a prominent marine biologist.
We report our first results on comparing the variations of the solar internal rotation with solar... more We report our first results on comparing the variations of the solar internal rotation with solar activity, as predicted by non-linear solar dynamo modelling, with helioseismic measurements using the SOHO MDI data.
Abstract: The second of the annual BritGrav meetings on current research in Gravitational Physics... more Abstract: The second of the annual BritGrav meetings on current research in Gravitational Physics in Britain took place at the School of Mathematical Sciences of Queen Mary, University of London on June 10/11, 2002. 47 plenary talks of 12min duration were given. We make available the abstracts of the talks and the references to the electronic preprints at arXiv. org where they exist.
We briefly summarise and further discuss the observational implications of the model-independent ... more We briefly summarise and further discuss the observational implications of the model-independent scheme recently put forward by us for the reconstruction of dark energy. The scheme employs rather weak geometrical features of the luminosity-distance relation motivated by recent observations. Using the SNLS supernovae data, the reconstructed luminosity-distance curves best fitting the data are shown to favour a Universe with a varying dark energy density, expanding at a slower rate than the ΛCDM model. The ΛCDM model. however, cannot be ruled out at high significance levels, in line with other recent reconstructions. We highlight the degeneracy concerning the CDM density parameter Ωm 0 , which acts as a barrier against a conclusive determination of whether the dark agency is the cosmological constant.
arXiv: General Relativity and Quantum Cosmology, 2015
We argue against current proposals concerning the non-existence of time. We point out that a larg... more We argue against current proposals concerning the non-existence of time. We point out that a large number of these proposals rely, at least implicitly, on the assumption of `closure' (or `partial closure') of the laws of Physics. I.e. the assumption that laws of Physics as they are known today are either complete (and hence closed) or that they possess features that a hypothetical future `complete' theory must share (and hence are partially closed). Given that the assumption of closure of laws of Physics can never be verified operationally, it cannot justifiably be used to support the claim for non-existence of time. Some approaches against time are `timeless' at the primary level for the universe as a whole. In these approaches time arises at a secondary level, mostly in the sense of `time being abstracted from change'. On the other hand, there are other approaches that deny the existence of time altogether. We argue that metaphysical arguments of this type - si...
We explore some fundational issues regarding the splitting of D-dimensional EFE's w.r.t timel... more We explore some fundational issues regarding the splitting of D-dimensional EFE's w.r.t timelike and spacelike (D-1)-dimensional hypersurfaces, first without and then with thin matter sheets such as branes. We begin to implement methodology, that is well-established for the GR CP and IVP, in the new field of GR-based braneworlds, identifying and comparing many different choices of procedure. We abridge fragmentary parts of the literature of embeddings, putting the Campbell--Magaard theorem into context. We recollect and refine arguments why York and not elimination methods are used for the GR IVP. We compile a list of numerous mathematical and physical impasses to using timelike splits, whereas spacelike splits are known to be well-behaved. We however pursue both options to make contact with the current braneworld literature which is almost entirely based on timelike splits. We look at the Shiromizu-Maeda -Sasaki braneworld by means of reformulations which emphasize different as...
We study the dynamics of states perturbatively expanded about a harmonic system of loop quantum c... more We study the dynamics of states perturbatively expanded about a harmonic system of loop quantum cosmology, exhibiting a bounce. In particular, the evolution equations for the first and second order moments of the system are analyzed. These moments back-react on the trajectories of the expectation values of the state and hence alter the energy density at the bounce. This analysis is performed for isotropic loop quantum cosmology coupled to a scalar field with a small but non-zero constant potential, hence in a regime in which the kinetic energy of matter dominates. Analytic restrictions on the existence of dynamical coherent states and the meaning of semi-classicality within these systems are discussed. A numerical investigation of the trajectories of states that remain semi-classical across the bounce demonstrates that, at least for such states, the bounce persists and that its properties are similar to the standard case, in which the moments of the states are entirely neglected. However the bounce density does change, implying that a quantum bounce may not be guaranteed to happen when the potential is no longer negligible.
Global symmetries of the string effective action are employed to generate tilted, homogeneous Bia... more Global symmetries of the string effective action are employed to generate tilted, homogeneous Bianchi type VI h string cosmologies from a previously known stiff perfect fluid solution to Einstein gravity. The dilaton field is not constant on the surfaces of homogeneity. The future asymptotic state of the models is interpreted as a plane wave and is itself an exact solution to the string equations of motion to all orders in the inverse string tension. An inhomogeneous generalization of the Bianchi type III model is also found.
Positively-curved, oscillatory universes are studied within the context of Loop Quantum Cosmology... more Positively-curved, oscillatory universes are studied within the context of Loop Quantum Cosmology subject to a consistent semi-classical treatment. The semi-classical effects are reformulated in terms of an effective phantom fluid with a variable equation of state. In cosmologies sourced by a massless scalar field, these effects lead to a universe that undergoes ever-repeating cycles of expansion and contraction. The presence of a self-interaction potential for the field breaks the symmetry of the cycles and can enable the oscillations to establish the initial conditions for successful slow-roll inflation, even when the field is initially at the minimum of its potential with a small kinetic energy. The displacement of the field from its minimum is enhanced for lower and more natural values of the parameter that sets the effective quantum gravity scale. For sufficiently small values of this parameter, the universe can enter a stage of eternal self-reproduction.
In loop quantum gravity, modifications to the geometrical density cause a self-interacting scalar... more In loop quantum gravity, modifications to the geometrical density cause a self-interacting scalar field to accelerate away from a minimum of its potential. In principle, this mechanism can generate the conditions that subsequently lead to slow-roll inflation. The consequences for this mechanism of various quantization ambiguities arising within loop quantum cosmology are considered. For the case of a quadratic potential, it is found that some quantization procedures are more likely to generate a phase of slow-roll inflation. In general, however, loop quantum cosmology is robust to ambiguities in the quantization and extends the range of initial conditions for inflation.
We make a systematic study of the cosmological dynamics for a number of f (R) gravity theories in... more We make a systematic study of the cosmological dynamics for a number of f (R) gravity theories in Palatini formalism, using phase space analysis as well as numerical simulations. Considering homogeneous and isotropic models, we find a number of interesting results: (i) models based on theories of the type (a) f (R) = R − β/R n and (b) f (R) = R + αln R − β, unlike the metric formalism, are capable of producing the sequence of radiation-dominated, matter-dominated and de-Sitter periods, and (ii) models based on theories of the type (c) f (R) = R + αR m − β/R n can produce early as well as late accelerating phases but an early inflationary epoch does not seem to be compatible with the presence of a subsequent radiation-dominated era. Thus for the classes of models considered here, we have been unable to find the sequence of all four dynamical epochs required to account for the complete cosmological dynamics, even though three out of four phases are possible. We also place observational constraints on these models using the recently released supernovae data by the Supernova Legacy Survey as well as the baryon acoustic oscillation peak in the SDSS luminous red galaxy sample and the CMB shift parameter. The best-fit values are found to be n = 0.027, α = 4.63 for the models based on (a) and α = 0.11, β = 4.62 for the models based on (b), neither of which are significantly preferred over the ΛCDM model. Moreover, the logarithmic term alone is not capable of explaining the late acceleration. The models based on (c) are also consistent with the data with suitable choices of their parameters. We also find that some of the models for which the radiation-dominated epoch is absent prior to the matter-dominated era also fit the data. The reason for this apparent contradiction is that the combination of the data considered here does not place stringent enough constraints on the cosmological evolution prior to the decoupling epoch, which highlights the importance of our combined theoretical-observational approach to constrain models.
Families of anisotropic and inhomogeneous string cosmologies containing non-trivial dilaton and a... more Families of anisotropic and inhomogeneous string cosmologies containing non-trivial dilaton and axion fields are derived by applying the global symmetries of the string effective action to a generalized Einstein-Rosen metric. The models exhibit a twodimensional group of Abelian isometries. In particular, two classes of exact solutions are found that represent inhomogeneous generalizations of the Bianchi type VI h cosmology. The asymptotic behaviour of the solutions is investigated and further applications are briefly discussed.
We take a critical look at a recent conjecture concerning the past attractor in the pre-big-bang ... more We take a critical look at a recent conjecture concerning the past attractor in the pre-big-bang scenario. We argue that the Milne universe is unlikely to be a general past attractor for such models and support this with a number of examples.
Journal of Cosmology and Astroparticle Physics, 2005
The geodesics of a spacetime seldom coincide with those of an embedded submanifold of codimension... more The geodesics of a spacetime seldom coincide with those of an embedded submanifold of codimension one. We investigate this issue for higher-dimensional general relativity-like models, firstly in the simpler case without branes to isolate which features are already present, and then in the more complicated case with branes. The framework in which we consider branes is general enough to include asymmetric braneworlds but not thick branes. We apply our results on geodesics to study both the equivalence principle and cosmological singularities. Among the models we study these considerations favour Z 2 symmetric braneworlds with a negative bulk cosmological constant.
Journal of Cosmology and Astroparticle Physics, 2012
We calculate the conditions required to produce a large local trispectrum during two-field slow-r... more We calculate the conditions required to produce a large local trispectrum during two-field slow-roll inflation. This is done by extending and simplifying the 'heat-map' approach developed by Byrnes et al. The conditions required to generate a large trispectrum are broadly the same as those that can produce a large bispectrum. We derive a simple relation between τ NL and f NL for models with separable potentials, and furthermore show that g NL and τ NL can be related in specific circumstances. Additionally, we interpret the heatmaps dynamically, showing how they can be used as qualitative tools to understand the evolution of non-Gaussianity during inflation. We also show how f NL , τ NL and g NL are sourced by generic shapes in the inflationary potential, namely ridges, valleys and inflection points.
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Papers by Reza Tavakol