MG15 - Talk detail

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In the context of single-field inflation, the conservation of the curvature perturbation on comoving slices, $\R_c$, on super-horizon scales is one of the assumptions necessary to derive the consistency condition between the squeezed limit of the bispectrum and the spectrum of the primordial curvature perturbation. However, the conservation of $\R_c$ holds only after the perturbation has reached the adiabatic limit where the constant mode of $\R_c$ dominates over the other (usually decaying) mode. In this case, the non-adiabatic pressure perturbation defined in the thermodynamic sense, δPnad≡δP−c2wδρ where c2w=P˙/ρ˙, usually becomes also negligible on superhorizon scales. Therefore one might think that the adiabatic limit is the same as thermodynamic adiabaticity. This is in fact not true. In other words, thermodynamic adiabaticity is not a sufficient condition for the conservation of $\R_c$ on super-horizon scales. In this paper, we consider models that satisfy δPnad=0 on all scales, which we call global adiabaticity (GA), which is guaranteed if c2w=c2s, where cs is the phase velocity of the propagation of the perturbation. A known example is the case of ultra-slow-roll(USR) inflation in which c2w=c2s=1. In order to generalize USR we develop a method to find the Lagrangian of GA K-inflation models from the behavior of background quantities as functions of the scale factor. Applying this method we show that there indeed exists a wide class of GA models with c2w=c2s, which allows $\R_c$ to grow on superhorizon scales, and hence violates the non-Gaussianity consistency condition.

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Motivated by reported claims of the measurements of a variation of the fine structure constant α we consider a theory where the electric charge, and consequently α, is not a constant but depends on the Ricci scalar R. We study the cosmological implications of this theory, considering in particular the effects of dark energy and of a cosmological constant on the evolution of α. Some low-red shift expressions for the variation of α(z) are derived, showing the effects of the equation of state of dark energy on α and observing how future measurements of the variation of the fine structure constant could be used to determine indirectly the equation of state of dark energy and test this theory. In the case of a ΛCDM Universe, according to the current estimations of the cosmological parameters, the present value of the Ricci scalar is ≈10 smaller than its future asymptotic value determined by the value of the cosmological constant, setting also a bound on the future asymptotic value of α.

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Static coordinates can be convenient to solve the vacuum Einstein's equations in presence of spherical symmetry, but for cosmological applications comoving coordinates are more suitable to describe an expanding Universe, especially in the framework of cosmological perturbation theory (CPT). Using CPT we develop a method to transform static spherically symmetric (SSS) modifications of the de Sitter solution from static coordinates to the Newton gauge. We test the method with the Schwarzschild de Sitter (SDS) metric and then derive general expressions for the Bardeen's potentials for a class of SSS metrics obtained by adding to the de Sitter metric a term linear in the mass and proportional to a general function of the radius. Using the gauge invariance of the Bardeen's potentials we then obtain a gauge invariant definition of the turn around radius. We apply the method to an SSS solution of the Brans-Dicke theory, confirming the results obtained independently by solving the perturbation equations in the Newton gauge. The Bardeen's potentials are then derived for new SSS metrics involving logarithmic, power law and exponential modifications of the de Sitter metric. We also apply the method to SSS metrics which give flat rotation curves, computing the radial energy density profile in comoving coordinates in presence of a cosmological constant.

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The recent analysis of low-redshift supernovae (SN) has increased the apparent tension between the value of $H_0$ estimated from low and high redshift observations such as the cosmic microwave background (CMB) radiation. At the same time other observations have provided evidence of the existence of local radial inhomogeneities extending in different directions up to a redshift of about $0.07$. About $40\%$ of the Cepheids used for SN calibration are directly affected because are located along the directions of these inhomogeneities. We compute with different methods the effects of these inhomogeneities on the low-redshift luminosity and angular diameter distance using an exact solution of the Einstein's equations, linear perturbation theory and a low-redshift expansion. We confirm that at low redshift the dominant effect is the non relativist Doppler redshift correction, which is proportional to the volume averaged density contrast and to the comoving distance from the center. We derive a new simple formula relating directly the luminosity distance to the monopole of the density contrast, which does not involve any metric perturbation. We then use it to develop a new inversion method to reconstruct the monopole of the density field from the deviations of the redshift uncorrected observed luminosity distance respect to the $\Lambda CDM$ prediction based on cosmological parameters obtained from large scale observations. The inversion method confirms the existence of inhomogeneities whose effects were not previously taken into account because the $2M++$ \cite{2MPP} density field maps used to obtain the peculiar velocity \cite{Carrick:2015xza} for redshift correction were for $z\leq 0.06$, which is not a sufficiently large scale to detect the presence of inhomogeneities extending up to $z=0.07$. The inhomogeneity does not affect the high redshift luminosity distance because the volume averaged density contrast tends to zero asymptotically, making the value of $H_0^{CMB}$ obtained from CMB observations insensitive to any local structure. The inversion method can provide a unique tool to reconstruct the density field at high redshift where only SN data is available, and in particular to normalize correctly the density field respect to the average large scale density of the Universe.

Pdf file

Session

Accepted

Yes

Order

Time

Talk

Title

Abstract

The recent analysis of low-redshift supernovae (SN) has increased the apparent tension between the value of H0 estimated from low and high redshift observations such as the cosmic microwave background (CMB) radiation. At the same time other observations have provided evidence of the existence of local radial inhomogeneities extending in different directions up to a redshift of about 0.07. About 40% of the Cepheids used for SN calibration are directly affected because are located along the directions of these inhomogeneities. We derive a new simple formula relating directly the luminosity distance to the monopole of the density contrast, which does not involve any metric perturbation. We then use it to develop a new inversion method to reconstruct the monopole of the density field from the deviations of the redshift uncorrected observed luminosity distance respect to the ΛCDM prediction based on cosmological parameters obtained from large scale observations. The inversion method confirms the existence of inhomogeneities whose effects were not previously taken into account because the 2M++ density field maps used to obtain the peculiar velocity for redshift correction were for z≤0.06, which is not a sufficiently large scale to detect the presence of inhomogeneities extending up to z=0.07. The inhomogeneity does not affect the high redshift luminosity distance because the volume averaged density contrast tends to zero asymptotically, making the value of HCMB0 obtained from CMB observations insensitive to any local structure. The inversion method can provide a unique tool to reconstruct the density field at high redshift where only SN data is available, and in particular to normalize correctly the density field respect to the average large scale density of the Universe.

Pdf file

Session

Accepted

Yes

Order

Time

Talk

Title

Abstract

We introduce two new effective quantities for the study of comoving curvature perturbations ζ : the space dependent effective sound speed (SESS) and the momentum dependent effective sound speed (MESS) . We use the SESS and the MESS to derive a new set of equations which can be applied to multi-fields systems and modified gravity theories. We show that this approach is completely equivalent to the standard one and it has the advantage of requiring to solve only one differential equation for ζ instead of a system, without the need of explicitly computing the evolution of entropy perturbations. The equations are valid for perturbations respect to any arbitrary flat spatially homogeneous background, including any inflationary and bounce model. As an application we derive the equation for ζ for multi-fields KGB models and show that observed features of the primordial curvature perturbation spectrum are compatible with the effects of an appropriate local variation of the MESS in momentum space. The MESS is the natural quantity to parametrize in a model independent way the effects produced on curvature perturbations by multi-fields systems and modified gravity theories and could be conveniently used in the analysis of LSS observations, such as the ones from the upcoming EUCLID mission or CMB radiation measurements.

Pdf file

Session

Accepted

Yes

Order

Time

Talk

Title

Abstract

We introduce two new effective quantities for the study of comoving curvature perturbations ζ : the space dependent effective sound speed (SESS) and the momentum dependent effective sound speed (MESS) . We use the SESS and the MESS to derive a new set of equations which can be applied to multi-fields systems and modified gravity theories. We show that this approach is completely equivalent to the standard one and it has the advantage of requiring to solve only one differential equation for ζ instead of a system, without the need of explicitly computing the evolution of entropy perturbations. The equations are valid for perturbations respect to any arbitrary flat spatially homogeneous background, including any inflationary and bounce model. As an application we derive the equation for ζ for multi-fields KGB models and show that observed features of the primordial curvature perturbation spectrum are compatible with the effects of an appropriate local variation of the MESS in momentum space. The MESS is the natural quantity to parametrize in a model independent way the effects produced on curvature perturbations by multi-fields systems and modified gravity theories and could be conveniently used in the analysis of LSS observations, such as the ones from the upcoming EUCLID mission or CMB radiation measurements.

Pdf file

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