arXiv subjects

L. R. Abramo

Publications and source records attributed to L. R. Abramo.

32 records · Page 2Linked to original sources

arXiv2007

Structure formation in the presence of dark energy perturbations

We study non-linear structure formation in the presence of dark energy. The influence of dark energy on the growth of large-scale cosmological structures is exerted both through its background effect on the expansion rate, and through its perturbations as well. In order to compute the rate of formation of massive objects we employ the Spherical Collapse formalism, which we generalize to include fluids with pressure. We show that the resulting non-linear evolution equations are identical to the ones obtained in the Pseudo-Newtonian approach to cosmological perturbations, in the regime where an equation of state serves to describe both the background pressure relative to density, and the pressure perturbations relative to the density perturbations as well. We then consider a wide range of constant and time-dependent equations of state (including phantom models) parametrized in a standard way, and study their impact on the non-linear growth of structure. The main effect is the formation of dark energy structure associated with the dark matter halo: non-phantom equations of state induce the formation of a dark energy halo, damping the growth of structures; phantom models, on the other hand, generate dark energy voids, enhancing structure growth. Finally, we employ the Press-Schechter formalism to compute how dark energy affects the number of massive objects as a function of redshift.

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arXiv2003

Dynamical study of the singularities of gravity in the presence of non-minimally coupled scalar fields

We investigate the dynamics of Einstein equations in the vicinity of the two recently described types of singularity of anisotropic and homogeneous cosmological models described by the action $$ S=\int d^4x \sqrt{-g}{F(ϕ)R - \partial_aϕ\partial^aϕ-2V(ϕ)}, $$ with general $F(ϕ)$ and $V(ϕ)$. The dynamical nature of each singularity is elucidated, and we show that both are, in general, dynamically unavoidable, reinforcing the unstable character of previous isotropic and homogeneous cosmological results obtained for the conformal coupling case.

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arXiv2003

A note on dualities in Einstein's gravity in the presence of a non-minimally coupled scalar field

We show that the action of Einstein's gravity with a scalar field coupled in a generic way to spacetime curvature is invariant under a particular set of conformal transformations. These transformations relate dual theories for which the effective couplings of the theory are scaled uniformly. In the simplest case, this class of dualities reduce to the S-duality of low-energy effective action of string theory.

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arXiv2001

A Scalar Measure Of The Local Expansion Rate

We define a scalar measure of the local expansion rate based on how astronomers determine the Hubble constant. Our observable is the inverse conformal d'Alembertian acting on a unit ``standard candle.'' Because this quantity is an integral over the past lightcone of the observation point it provides a manifestly causal and covariant technique for averaging over small fluctuations. For an exactly homogeneous and isotropic spacetime our scalar gives minus one half times the inverse square of the Hubble parameter. Our proposal is that it be assigned this meaning generally and that it be employed to decide the issue of whether or not there is a significant quantum gravitational back-reaction on inflation. Several techniques are discussed for promoting the scalar to a full invariant by giving a geometrical description for the point of observation. We work out an explicit formalism for evaluating the invariant in perturbation theory. The results for two simple models are presented in subsequent papers.

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arXiv2001

No One Loop Back_Reaction In Chaotic Inflation

We use an invariant operator to study the quantum gravitational back-reaction to scalar perturbations during chaotic inflation. Our operator is the inverse covariant d'Alembertian expressed as a function of the local value of the inflaton. In the slow roll approximation this observable gives $-1/(2 H^2)$ for an arbitrary homogeneous and isotropic geometry, hence it is a good candidate for measuring the local expansion rate even when the spacetime is not perfectly homogeneous and isotropic. Corrections quadratic in the scalar creation and annihilation operators of the initial value surface are included using the slow-roll and long wavelength approximations. The result is that all terms which could produce a significant secular back-reaction cancel from the operator, before one even takes its expectation value. Although it is not relevant to the current study, we also develop a formalism for using stochastic samples to study back-reaction.

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arXiv2001

Back-Reaction Is For Real

We demonstrate the existence of a secular back-reaction on inflation using a simple scalar model. The model consists of a massless, minimally coupled scalar with a quartic self-interaction which is a spectator to $Λ$-driven inflation. To avoid problems with coincident propagators, and to make the scalars interact more like gravitons, we impose a covariant normal ordering prescription which has the effect of removing tadpole graphs. This version of the theory exhibits a secular slowing at three loop order due to interactions between virtual infrared scalars which are ripped apart by the inflating background. The effect is quantified using an invariant observable and all orders bounds are given. We also argue that, although stochastic effects can have either sign, the slowing mechanism is superimposed upon them.

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arXiv2001

Attractors and Isocurvature Perturbations in Quintessence Models

We investigate the evolution of cosmological perturbations in scenarios with a quintessence scalar field, both analytically and numerically. In the tracking regime for quintessence, we find the long wavelength solutions for quintessential perturbations. We discuss the possibility of isocurvature modes generated by the quintessence sector and their impact on observations.

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arXiv1999

Back Reaction of Gravitational Radiation on the Schwarzschild Black Hole

We address some of the issues that appear in the study of back reaction in Schwarzschild backgrounds. Our main object is the effective energy-momentum tensor (EEMT) of gravitational perturbations. It is commonly held that only asymptotically flat or radiation gauges can be employed for these purposes. We show that the traditional Regge-Wheeler gauge for the perturbations of the Schwarszchild metric can also be used for computing physical quantities both at the horizon and at infinity. In particular, we find that the physically relevant components of the EEMT of gravitational perturbations have the same asymptotic behaviour as the stress-energy tensor of a scalar field in the Schwarzschild background, even though some of the metric components themselves diverge.

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arXiv1999

Energy density and pressure of long wavelength gravitational waves

Inflation leads us to expect a spectrum of gravitational waves (tensor perturbations) extending to wavelengths much bigger than the present observable horizon. Although these gravity waves are not directly observable, the energy density that they contribute grows in importance during the radiation- and dust-dominated ages of the universe. We show that the back reaction of tensor perturbations during matter domination is limited from above, since gravitational waves of wavelength $λ$ have a share of the total energy density $Δρ(λ)/ρ$ during matter domination that is at most equal to the share of the total energy density that they had when the mode $λ$ exited the Hubble radius $H^{-1}$ during inflation. This work is to be contrasted to that of Sahni, who analyzed the energy density of gravity waves only insofar as their wavelengths are smaller than $H^{-1}$. Such a cut-off in the spectral energy of gravity waves leads to the breakdown of energy conservation, and we show that this anomaly is eliminated simply by taking into account the energy density and pressure of long wavelength gravitational waves as well as short wavelength ones.

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arXiv1998

One Loop Back Reaction On Chaotic Inflation

We extend, for the case of a general scalar potential, the inflaton-graviton Feynman rules recently developed by Iliopoulos {\it et al.} As an application we compute the leading term, for late co-moving times, of the one loop back reaction on the expansion rate for $V(ϕ) = \frac12 m^2 ϕ^2$. This is expressed as the logarithmic time derivative of the scale factor in the coordinate system for which the expectation value of the metric has the form: $<0 | g_{μν}({\bar t},{\vec x}) | 0 > dx^μ dx^ν = - d{\bar t}^2 + a^2({\bar t}) d{\vec x} \cdot d{\vec x}$. This quantity should be a gauge independent observable. Our result for it agrees exactly with that inferred from the effect previously computed by Mukhanov {\it et al.} using canonical quantization. It is significant that the two calculations were made with completely different schemes for fixing the gauge, and that our computation was done using the standard formalism of covariant quantization. This should settle some of the issues recently raised by Unruh.

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arXiv1998

One Loop Back Reaction On Power Law Inflation

We consider quantum mechanical corrections to a homogeneous, isotropic and spatially flat geometry whose scale factor expands classically as a general power of the co-moving time. The effects of both gravitons and the scalar inflaton are computed at one loop using the manifestly causal formalism of Schwinger with the Feynman rules recently developed by Iliopoulos {\it et al.} We find no significant effect, in marked contrast with the result obtained by Mukhanov {\it et al.} for chaotic inflation based on a quadratic potential. By applying the canonical technique of Mukhanov {\it et al.} to the exponential potentials of power law inflation, we show that the two methods produce the same results, within the approximations employed, for these backgrounds. We therefore conclude that the shape of the inflaton potential can have an enormous impact on the one loop back-reaction.

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arXiv1998

Cosmological Density Perturbations From A Quantum Gravitational Model Of Inflation

We derive the implications for anisotropies in the cosmic microwave background following from a model of inflation in which a bare cosmological constant is gradually screened by an infrared process in quantum gravity. The model predicts that the amplitude of scalar perturbations is $A_S = (2.0 \pm .2) \times 10^{-5}$, that the tensor-to-scalar ratio is $r \approx 1.7 \times 10^{-3}$, and that the scalar and tensor spectral indices are $n \approx .97$ and $n_T \approx -2.8 \times 10^{-4}$, respectively. By comparing the model's power spectrum with the COBE 4-year RMS quadrupole, the mass scale of inflation is determined to be $M = (.72 \pm .03) \times 10^{16}~{\rm GeV}$. At this scale the model produces about $10^8$ e-foldings of inflation, so another prediction is $Ω= 1$.

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arXiv1997

The Energy-Momentum Tensor for Cosmological Perturbations

We study the effective energy-momentum tensor (EMT) for cosmological perturbations and formulate the gravitational back-reaction problem in a gauge invariant manner. We analyze the explicit expressions for the EMT in the cases of scalar metric fluctuations and of gravitational waves and derive the resulting equations of state. The formalism is applied to investigate the back-reaction effects in chaotic inflation. We find that for long wavelength scalar and tensor perturbations, the effective energy density is negative and thus counteracts any pre-existing cosmological constant. For scalar perturbations during an epoch of inflation, the equation of state is de Sitter-like.

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arXiv1997

Back Reaction of Gravitational Perturbations

The back reaction of gravitational perturbations in a homogeneous background is determined by an effective energy-momentum tensor quadratic in the perturbations. We show that this nonlinear feedback effect is important in the case of long wavelength scalar perturbations in inflationary universe models. We also show how to solve an old problem concerning the gauge dependence of the effective energy-momentum tensor of perturbations.

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