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Jerome Martin

Publications and source records attributed to Jerome Martin.

At least 127 records · Page 7Linked to original sources
arXiv2001

Best Unbiased Estimators for the Three-Point Correlators of the Cosmic Microwave Background Radiation

Measuring the three-point correlators of the Cosmic Microwave Background (CMB) anisotropies could help to get a handle on the level of non-Gaussianity present in the observational datasets and therefore would strongly constrain models of the early Universe. However, typically, the expected non-Gaussian signal is very small. Therefore, one has to face the problem of extracting it from the noise, in particular from the `cosmic variance' noise. For this purpose, one has to construct the best unbiased estimators for the three-point correlators that are needed for concrete detections of non-Gaussian features. In this article, we study this problem for both the CMB third moment and the CMB angular bispectrum. We emphasize that the knowledge of the best estimator for the former does not permit one to infer the best estimator for the latter and vice versa. We present the corresponding best unbiased estimators in both cases and compute their corresponding cosmic variances.

astro-ph↗
arXiv2000

Slow-roll inflation and CMB anisotropy data

We emphasize that the estimation of cosmological parameters from cosmic microwave background (CMB) anisotropy data, such as the recent high resolution maps from BOOMERanG and MAXIMA-1, requires assumptions about the primordial spectra. The latter are predicted from inflation. The physically best-motivated scenario is that of slow-roll inflation. However, very often, the unphysical power-law inflation scenario is (implicitly) assumed in the CMB data analysis. We show that the predicted multipole moments differ significantly in both cases. We identify several misconceptions present in the literature (and in the way inflationary relations are often combined in popular numerical codes). For example, we do not believe that, generically, inflation predicts the relation n_S - 1 = n_T for the spectral indices of scalar and tensor perturbations or that gravitational waves are negligible. We calculate the CMB multipole moments for various values of the slow-roll parameters and demonstrate that an important part of the space of parameters (n_S, n_T) has been overlooked in the CMB data analysis so far.

astro-ph↗
arXiv2000

New exact solutions for inflationary cosmological perturbations

From a general ansatz for the effective potential of cosmological perturbations we find new, exact solutions in single-scalar-field inflation: a three parameter family of exact inflationary solutions that encompasses all exact solutions that have been known previously (power-law inflation, Easther's model, and a generalised version of Starobinsky's solution). The main feature of this new family is that the spectral indices are scale dependent.

astro-ph↗
arXiv2000

Geodesic Deviation in Kaluza-Klein Theories

We study in detail the equations of the geodesic deviation in multidimensional theories of Kaluza-Klein type. We show that their 4-dimensional space-time projections are identical with the equations obtained by direct variation of the usual geodesic equation in the presence of the Lorentz force, provided that the fifth component of the deviation vector satisfies an extra constraint derived here.

gr-qc↗
arXiv2000

The precision of slow-roll predictions for the CMBR anisotropies

Inflationary predictions for the anisotropy of the cosmic microwave background radiation (CMBR) are often based on the slow-roll approximation. We study the precision with which the multipole moments of the temperature two-point correlation function can be predicted by means of the slow-roll approximation. We ask whether this precision is good enough for the forthcoming high precision observations by means of the MAP and Planck satellites. The error in the multipole moments due to the slow-roll approximation is demonstrated to be bigger than the error in the power spectrum. For power-law inflation with $n_S=0.9$ the error from the leading order slow-roll approximation is $\approx 5%$ for the amplitudes and $\approx 20%$ for the quadrupoles. For the next-to-leading order the errors are within a few percent. The errors increase with $|n_S - 1|$. To obtain a precision of 1% it is necessary, but in general not sufficient, to use the next-to-leading order. In the case of power-law inflation this precision is obtained for the spectral indices if $|n_S - 1| < 0.02$ and for the quadrupoles if $|n_S - 1| < 0.15$ only. The errors in the higher multipoles are even larger than those for the quadrupole, e.g. $\approx 15%$ for l=100, with $n_S = 0.9$ at the next-to-leading order. We find that the accuracy of the slow-roll approximation may be improved by shifting the pivot scale of the primordial spectrum (the scale at which the slow-roll parameters are fixed) into the regime of acoustic oscillations. Nevertheless, the slow-roll approximation cannot be improved beyond the next-to-leading order in the slow-roll parameters.

astro-ph↗
arXiv2000

High Energy Physics and Quintessence

It is shown that any realistic model of quintessence should be based on Supergravity (SUGRA) since the value of the quintessence field on the attractor is approximately the Planck mass. Under very general assumptions, the typical shape of a SUGRA tracking potential is derived. Cosmological implications are investigated. In particular, it is demonstrated that, generically, the equation of state parameter is driven to a value close to -1 in agreement with recent observations.

astro-ph↗
arXiv2000

Exhaustive Study of Cosmic Microwave Background Anisotropies in Quintessential Scenarios

Recent high precision measurements of the CMB anisotropies performed by the BOOMERanG and MAXIMA-1 experiments provide an unmatched set of data allowing to probe different cosmological models. Among these scenarios, motivated by the recent measurements of the luminosity distance versus redshift relation for type Ia supernovae, is the quintessence hypothesis. It consists in assuming that the acceleration of the Universe is due to a scalar field whose final evolution is insensitive to the initial conditions. Within this framework we investigate the cosmological perturbations for two well-motivated potentials: the Ratra-Peebles and the SUGRA tracking potentials. We show that the solutions of the perturbed equations possess an attractor and that, as a consequence, the insensitivity to the initial conditions is preserved at the perturbed level. Then, we study the predictions of these two models for structure formation and CMB anisotropies and investigate the general features of the multipole moments in the presence of quintessence. We also compare the CMB multipoles calculated with the help of a full Boltzmann code with the BOOMERanG and MAXIMA-1 data. We pay special attention to the location of the second peak and demonstrate that it significantly differs from the location obtained in the cosmological constant case. Finally, we argue that the SUGRA potential is compatible with all the recent data with a standard values of the cosmological parameters. In particular, it fits the MAXIMA-1 data better than a cosmological constant or the Ratra-Peebles potential.

astro-ph↗
arXiv2000

Cosmic microwave background bispectrum and slow roll inflation

Recent tentative findings of non-Gaussian structure in the COBE-DMR dataset have triggered renewed attention to candidate models from which such intrinsic signature could arise. In the framework of slow roll inflation with built-in non linearities in the inflaton field evolution we present expressions for both the cosmic microwave background (CMB) skewness and the full angular bispectrum ${\cal C}_{\ell_1 \ell_2 \ell_3}$ in terms of the slow roll parameters. We use an estimator for the angular bispectrum recently proposed in the literature and calculate its variance for an arbitrary $\ell_i$ multipole combination. We stress that a real detection of non-Gaussianity in the CMB would imply that an important component of the anisotropies arises from processes {\it other} than primordial quantum fluctuations. We further investigate the behavior of the signal-to-(theoretical) noise ratio and demonstrate for generic inflationary models that it decreases in the limited range of small-$\ell$'s considered for increasing multipole $\ell$ while the opposite applies for the standard ${\cal C}_{\ell}$'s.

astro-ph↗
arXiv1999

The Robustness of Quintessence

Recent observations seem to suggest that our Universe is accelerating implying that it is dominated by a fluid whose equation of state is negative. Quintessence is a possible explanation. In particular, the concept of tracking solutions permits to adress the fine-tuning and coincidence problems. We study this proposal in the simplest case of an inverse power potential and investigate its robustness to corrections. We show that quintessence is not affected by the one-loop quantum corrections. In the supersymmetric case where the quintessential potential is motivated by non-perturbative effects in gauge theories, we consider the curvature effects and the Kähler corrections. We find that the curvature effects are negligible while the Kähler corrections modify the early evolution of the quintessence field. Finally we study the supergravity corrections and show that they must be taken into account as $Q\approx m_{\rm Pl}$ at small red-shifts. We discuss simple supergravity models exhibiting the quintessential behaviour. In particular, we propose a model where the scalar potential is given by $V(Q)=\frac{Λ^{4+α}}{Q^α}e^{\fracκ{2}Q^2}$. We argue that the fine-tuning problem can be overcome if $α\ge 11$. This model leads to $ω_Q\approx -0.82$ for $Ω_{\rm m}\approx 0.3$ which is in good agreement with the presently available data.

astro-ph↗
arXiv1999

Cosmological Implications of the Supergravity Tracking Potential

It is demonstrated that any realistic model of quintessence should be based on Supergravity since, when the scalar field is on tracks today, $Q\approx m_{\rm Pl}$. This improves the agreement between theoretical predictions and the current observations. In particular, a generic property is that ratio $ω_{\rm Q}\equiv p_{\rm Q}/ρ_{\rm Q}$ is pushed towards -1. A string-inspired model is proposed where the potential is given by $V(Q)= \frac{Λ^{4+α}}{Q^α}e^{\fracκ{2}Q^2}$. The model predicts $ω_{\rm Q}\approx -0.82$, a value less that one sigma from the current likehood value.

astro-ph↗
arXiv1999

Quintessence and Supergravity

In the context of quintessence, the concept of tracking solutions allows to address the fine-tuning and coincidence problems. When the field is on tracks today, one has $Q\approx m_{\rm Pl}$ demonstrating that, generically, any realistic model of quintessence must be based on supergravity. We construct the most simple model for which the scalar potential is positive. The scalar potential deduced from the supergravity model has the form $V(Q)=\frac{Λ^{4+α}}{Q^α}e^{\fracκ{2}Q^2}$. We show that despite the appearence of positive powers of the field, the coincidence problem is still solved. If $α\ge 11$, the fine-tuning problem can be overcome. Moreover, due to the presence of the exponential term, the value of the equation of state, $ω_Q$, is pushed towards the value -1 in contrast to the usual case for which it is difficult to go beyond $ω_Q\approx -0.7$. For $Ω_{\rm m}\approx 0.3$, the model presented here predicts $ω_Q\approx -0.82$. Finally, we establish the $Ω_{\rm m}-ω_Q$ relation for this model.

astro-ph↗
arXiv1999

Quantum Cosmology and Open Universes

Quantum creation of Universes with compact spacelike sections that have curvature $k$ either closed, flat or open, i.e. $k=\pm1,0$ are studied. In the flat and open cases, the superpotential of the Wheeler De Witt equation is significantly modified, and as a result the qualitative behaviour of a typical wavefunction differs from the traditional closed case. Using regularity arguments, it is shown that the only consistent state for the wavefunction is the Tunneling one. By computing the quantum probabilities for the curvature of the sections, it is shown that quantum cosmology actually favours that the Universe be open, $k=-1$. In all cases sufficient inflation $\sim 60$ e-foldings is predicted: this is an improvement over classical measures that generally are ambiguous as to whether inflation is certain to occur.

gr-qc↗
arXiv1999

Non-Vacuum Initial States for Cosmological Perturbations of Quantum-Mechanical Origin

In the context of inflation, non-vacuum initial states for cosmological perturbations that possess a built in scale are studied. It is demonstrated that this assumption leads to a falsifiable class of models. The question of whether they lead to conflicts with the available observations is addressed. For this purpose, the power spectrum of the Bardeen potential operator is calculated and compared with the CMBR anisotropies measurements and the redshift surveys of galaxies and clusters of galaxies. Generic predictions of the model are: a high first acoustic peak, the presence of a bump in the matter power spectrum and non-Gaussian statistics. The details are controlled by the number of quanta in the non-vacuum initial state. Comparisons with observations show that there exists a window for the free parameters such that good agreement between the data and the theoretical predictions is possible. However, in the case where the initial state is a state with a fixed number of quanta, it is shown that this number cannot be greater than a few. On the other hand, if the initial state is a quantum superposition, then a larger class of initial states could account for the observations, even though the state cannot be too different from the vacuum. Planned missions such as the MAP and Planck satellites and the Sloan Survey, will demonstrate whether the new class of models proposed here represents a viable alternative to the standard theory.

astro-ph↗
arXiv1998

Predictions of inflation: the slow roll approximation vs. exact results

Inflation predicts the generation of cosmological perturbations. Usually, the power spectra for the scalar and tensor modes are calculated with help of the slow roll approximation. In the case of power law inflation an exact result is available. We compare the predictions for the cosmic microwave background anisotropies from the slow roll approximation with the exact results from power law inflation. We find that the so-called consistency check from the slow roll approximation, $C_2^T/C_2^S \approx -6.93 n_T$, may differ considerably from the exact result.

astro-ph↗
arXiv1998

Amplitude of superhorizon cosmological perturbations

We study the influence of reheating on super-horizon density perturbations and gravitational waves. We correct wrong claims [L. P. Grishchuk Phys. Rev. D 50, 7154 (1994) and gr-qc/9801011] about the joining of perturbations at cosmological transitions and about the quantization of cosmological perturbations.

gr-qc↗
arXiv1997

Topology Change in Canonical Quantum Cosmology

We develop the canonical quantization of a midisuperspace model which contains, as a subspace, a minisuperspace constituted of a Friedman-Lema\^ıtre-Robertson-Walker Universe filled with homogeneous scalar and dust fields, where the sign of the intrinsic curvature of the spacelike hypersurfaces of homogeneity is not specified, allowing the study of topology change in these hypersurfaces. We solve the Wheeler-DeWitt equation of the midisuperspace model restricted to this minisuperspace subspace in the semi-classical approximation. Adopting the conditional probability interpretation, we find that some of the solutions present change of topology of the homogeneous hypersurfaces. However, this result depends crucially on the interpretation we adopt: using the usual probabilistic interpretation, we find selection rules which forbid some of these topology changes.

gr-qc↗