The Hubble effective potential

2013

A generic homogenous and isotropic cosmology is investigated based on the scalar-tensor theory of gravitation involving general metric coupling and scalar potential functions. We show that for a broad class of such functions, the scalar gravitational field can be dynamically trapped using a recently suggested mechanism. The corresponding scalar potential can drive inflation, accelerating expansion in the early and late universe respectively, with features consistent with standard requirements. Remarkably, the inflationary phase admits a natural exit with a well-defined value of the Hubble parameter dictated by the duration of inflation in a parameter independent manner, regardless of the detailed forms of the metric coupling and scalar potential. For an inflation duration consistent with the GUT description of the early universe, the resulting Hubble parameter is found to be consistent with its observed value.

The Astrophysical Journal, 1994

We explore the possibility of describing our universe with a singularity-free, closed, spatially homogeneous and isotropic cosmological model, using only general relativity and a suitable equation of state which produces an inflationary era. A phase transition to a radiation-dominated era occurs as a consequence of boundary conditions expressing the assumption that the temperature cannot exceed the Planck value. We find that over a broad range of initial conditions, the predicted value of the Hubble parameter is approximately 47 km· s −1 · Mpc −1 . Inflation is driven by a scalar field, which must be conformally coupled to the curvature if the Einstein equivalence principle has to be satisfied. The form of the scalar field potential is derived, instead of being assumed a priori.

arXiv (Cornell University), 2012

We report the outcome of a 3-day workshop on the Hubble constant (H0) that took place during February 6-8 2012 at the Kavli Institute for Particle Astrophysics and Cosmology, on the campus of Stanford University †. The participants met to address the following questions. Are there compelling scientific reasons to obtain more precise and more accurate measurements of H0 than currently available? If there are, how can we achieve this goal? The answers that emerged from the workshop are (1) better measurements of H0 provide critical independent constraints on dark energy, spatial curvature of the Universe, neutrino physics, and validity of general relativity, (2) a measurement of H0 to 1% in both precision and accuracy, supported by rigorous error budgets, is within reach for several methods, and (3) multiple paths to independent determinations of H0 are needed in order to access and control systematics.

2012

In this paper, we consider the Universe deep inside of the cell of uniformity. At these scales, the Universe is filled with inhomogeneously distributed discrete structures (galaxies, groups and clusters of galaxies), which disturb the background Friedmann model. We propose mathematical models with conformally flat, hyperbolic and spherical spaces. For these models, we obtain the gravitational potential for an arbitrary number of randomly distributed inhomogeneities. In the cases of flat and hyperbolic spaces, the potential is finite at any point, including spatial infinity, and valid for an arbitrary number of gravitating sources. For both of these models, we investigate the motion of test masses (e.g., dwarf galaxies) in the vicinity of one of the inhomogeneities. We show that there is a distance from the inhomogeneity, at which the cosmological expansion prevails over the gravitational attraction and where test masses form the Hubble flow. For our group of galaxies, it happens at a few Mpc and the radius of the zero-acceleration sphere is of the order of 1 Mpc, which is very close to observations. Outside of this sphere, the dragging effect of the gravitational attraction goes very fast to zero.

Modern Physics Letters A, 2005

The existence of cosmological perturbations of wavelength larger than the Hubble radius is a generic prediction of the inflationary paradigm. We provide the derivation beyond perturbation theory of a conserved quantity which generalizes the linear comoving curvature perturbation. As a by-product, we show that super-Hubble-radius (super-Hubble) perturbations have no physical influence on local observables (e.g., the local expansion rate) if cosmological perturbations are of the adiabatic type. PACS numbers: 98.80.cq

arXiv: General Physics, 2018

By considering the expansion of space as an additional component of general relativity, a model is described that adds a Hubble curvature term as a new solution to the general equation. Correlation with the $\Lambda$CDM model was assessed using the extensive type~Ia supernovae (SNe~Ia) data with redshift corrected to the CMB, and recent baryonic acoustic oscillation (BAO) measures. For the SNe~Ia data, the modified GR and $\Lambda$CDM models differed by $^{+0.11}_{-0.15}~\mu_B$~mag. over $z_{cmb}=0.01-1.3$, with overall weighted RMS errors of $\pm0.136$ and $\pm0.151$ $\mu_B$~mag respectively. For the BAO measures, the weighted RMS errors were $\pm0.034$ and $\pm0.085$ Mpc with $H_0=67.6\pm0.25$ for the modified GR and $70.0\pm0.25$ for the $\Lambda$CDM models, over the range $z=0.106-2.36$. The derived GR metric accurately describes both the SNe Ia and the baryonic acoustic oscillation (BAO) observations without requiring dark matter or $w$-corrected dark energy while allowing the ...

Physical Review D

We study the cosmological constraints on the variation of Newton's constant and on post-Newtonian parameters for simple models of the scalar-tensor theory of gravity beyond the extended Jordan-Brans-Dicke theory. We restrict ourselves to an effectively massless scalar field with a potential V ∝ F 2 , where FðσÞ ¼ N 2 pl þ ξσ 2 is the coupling to the Ricci scalar considered. We derive the theoretical predictions for cosmic microwave background anisotropies and matter power spectra by requiring that the effective gravitational strength at present is compatible with the one measured in a Cavendish-like experiment and by assuming an adiabatic initial condition for scalar fluctuations. When comparing these models with Planck 2015 and a compilation of baryonic acoustic oscillations data, all these models accommodate a marginalized value for H 0 higher than in ΛCDM. We find no evidence for a statistically significant deviation from Einstein's general relativity. We find ξ < 0.064 (jξj < 0.011) at 95% CL for ξ > 0 (for ξ < 0, ξ ≠ −1=6). In terms of post-Newtonian parameters, we find 0.995 < γ PN < 1 and 0.99987 < β PN < 1 (0.997 < γ PN < 1 and 1 < β PN < 1.000011) for ξ > 0 (for ξ < 0). For the particular case of the conformal coupling, i.e., ξ ¼ −1=6, we find constraints on the post-Newtonian parameters of similar precision to those within the Solar System.

Journal of Cosmology and Astroparticle Physics, 2007

The European Physical Journal C, 2016

In order to estimate the effects of local structure on the Hubble parameter we calculate the lowredshift expansion for H(z) and δH H for an observer at the center of a spherically symmetric matter distribution in presence of a cosmological constant. We then test the accuracy of the formulae comparing them with fully relativistic non perturbative numerical calculations for different cases for the density profile. The low red-shift expansion we obtain gives results more precise than perturbation theory since is based on the use of an exact solution of Einstein's field equations. For larger density contrasts the low red-shift formulae accuracy improves respect to the perturbation theory accuracy because the latter is based on the assumption of a small density contrast, while the former does not rely on such assumption. The formulae can be used to take into account the effects on the Hubble expansion parameter due to the monopole component of the local structure. If the H(z) observations will show deviations from the ΛCDM prediction compatible with the formulae we have derived, this could be considered an independent evidence of the existence of a local inhomogeneity, and the formulae could be used to determine the characteristics of this local structure.

Journal of Cosmology and Astroparticle Physics, 2011

The calculation of the averaged Hubble expansion rate in an averaged perturbed Friedmann-Lemaître-Robertson-Walker cosmology leads to small corrections to the background value of the expansion rate, which could be important for measuring the Hubble constant from local observations. It also predicts an intrinsic variance associated with the finite scale of any measurement of H0, the Hubble rate today. Both the mean Hubble rate and its variance depend on both the definition of the Hubble rate and the spatial surface on which the average is performed. We quantitatively study different definitions of the averaged Hubble rate encountered in the literature by consistently calculating the backreaction effect at second order in perturbation theory, and compare the results. We employ for the first time a recently developed gauge-invariant definition of an averaged scalar. We also discuss the variance of the Hubble rate for the different definitions.