arXiv subjects

Alexei A. Starobinsky

Publications and source records attributed to Alexei A. Starobinsky.

At least 91 records · Page 5Linked to original sources

arXiv2007

Disappearing cosmological constant in f(R) gravity

For higher-derivative f(R) gravity where R is the Ricci scalar, a class of models is proposed which produce viable cosmology different from the LambdaCDM one at recent times and satisfy cosmological, Solar system and laboratory tests. These models have both flat and de Sitter space-times as particular solutions in the absence of matter. Thus, a cosmological constant is zero in flat space-time, but appears effectively in a curved one for sufficiently large R. A 'smoking gun' for these models would be small discrepancy in values of the slope of the primordial perturbation power spectrum determined from galaxy surveys and CMB fluctuations. On the other hand, a new problem for dark energy models based on f(R) gravity is pointed which is connected with possible overproduction of new massive scalar particles (scalarons) arising in this theory in the very early Universe.

astro-ph↗

arXiv2007

Smoothing Supernova Data to Reconstruct the Expansion History of the Universe and its Age

We propose a non-parametric method of smoothing supernova data over redshift using a Gaussian kernel in order to reconstruct important cosmological quantities including H(z) and w(z) in a model independent manner. This method is shown to be successful in discriminating between different models of dark energy when the quality of data is commensurate with that expected from the future SuperNova Acceleration Probe (SNAP). We find that the Hubble parameter is especially well-determined and useful for this purpose. The look back time of the universe may also be determined to a very high degree of accuracy (\lleq 0.2 %) in this method. By refining the method, it is also possible to obtain reasonable bounds on the equation of state of dark energy. We explore a new diagnostic of dark energy-- the `w-probe'-- which can be calculated from the first derivative of the data. We find that this diagnostic is reconstructed extremely accurately for different reconstruction methods even if Ω_m is marginalized over. The w-probe can be used to successfully distinguish between $Λ$CDM and other models of dark energy to a high degree of accuracy.

astro-ph↗

arXiv2006

Exploring the Properties of Dark Energy Using Type Ia Supernovae and Other Datasets

We reconstruct dark energy properties from two complementary supernova datasets -- the newly released Gold+HST sample and SNLS. The results obtained are consistent with standard $Λ$CDM model within $2σ$ error bars although the Gold+HST data favour evolving dark energy slightly more than SNLS. Using complementary data from baryon acoustic oscillations and the cosmic microwave background to constrain dark energy, we find that our results in this case are strongly dependent on the present value of the matter density $Ω_m$. Consequently, no firm conclusions regarding constancy or variability of dark energy density can be drawn from these data alone unless the value of $Ω_m$ is known to an accuracy of a few percent. However, possible variability is significantly restricted if this data is used in conjunction with supernova data.

astro-ph↗

arXiv2006

No realistic wormholes from ghost-free scalar-tensor phantom dark energy

It is proved that no wormholes can be formed in viable scalar-tensor models of dark energy admitting its phantom-like ($w < -1$) behaviour in cosmology, even in the presence of electric or magnetic fields, if the non-minimal coupling function $f(Φ)$ is everywhere positive and the scalar field $Φ$ itself is not a ghost. Some special static, spherically symmetric wormhole solutions may exist if $f(Φ)$ is allowed to reach zero or to become negative, so that the effective gravitational constant becomes negative in some region making the graviton a ghost. If $f$ remains non-negative, such solutions require severe fine tuning and a very peculiar kind of model. If $f < 0$ is allowed, it is argued (and confirmed by previous investigations) that such solutions are generically unstable under non-static perturbations, the instability appearing right near transition surfaces to negative $f$.

gr-qc↗

arXiv2006

Scalar-Tensor Models of Normal and Phantom Dark Energy

We consider the viability of dark energy (DE) models in the framework of the scalar-tensor theory of gravity, including the possibility to have a phantom DE at small redshifts $z$ as admitted by supernova luminosity-distance data. For small $z$, the generic solution for these models is constructed in the form of a power series in $z$ without any approximation. Necessary constraints for DE to be phantom today and to cross the phantom divide line $p=-ρ$ at small $z$ are presented. Considering the Solar System constraints, we find for the post-Newtonian parameters that $γ_{PN}<1$ and $γ_{PN,0}\approx 1$ for the model to be viable, and $β_{PN,0}>1$ (but very close to 1) if the model has a significantly phantom DE today. However, prospects to establish the phantom behaviour of DE are much better with cosmological data than with Solar System experiments. Earlier obtained results for a $Λ$-dominated universe with the vanishing scalar field potential are extended to a more general DE equation of state confirming that the cosmological evolution of these models rule them out. Models of currently fantom DE which are viable for small $z$ can be easily constructed with a constant potential; however, they generically become singular at some higher $z$. With a growing potential, viable models exist up to an arbitrary high redshift.

astro-ph↗

arXiv2005

Inflaton field potential producing the exactly flat spectrum of adiabatic perturbations

Presented is the exact solution of the problem of finding a potential of an inflaton scalar field for which adiabatic perturbations generated during a de Sitter (inflationary) stage in the early Universe have the exactly flat (or, the Harrison-Zeldovich) initial spectrum. This solution lies outside the scope of the slow-roll approximation and higher-order corrections to it. The potential found depends on two arbitrary physical constants, one of those determines an amplitude of perturbations. For small (zero) values of the other constant, a long (infinite) inflationary stage with slow rolling of the inflaton field exists.

astro-ph↗

arXiv2001

Cosmological perturbations from multi-field inflation in generalized Einstein theories

We study cosmological perturbations generated from quantum fluctuations in multi-field inflationary scenarios in generalized Einstein theories, taking both adiabatic and isocurvature modes into account. In the slow-roll approximation, explicit closed-form long-wave solutions for field and metric perturbations are obtained by the analysis in the Einstein frame. Since the evolution of fluctuations depends on specific gravity theories, we make detailed investigations based on analytic and numerical approaches in four generalized Einstein theories: the Jordan-Brans-Dicke (JBD) theory, the Einstein gravity with a non-minimally coupled scalar field, the higher-dimensional Kaluza-Klein theory, and the $R+R^2$ theory with a non-minimally coupled scalar field. We find that solutions obtained in the slow-roll approximation show good agreement with full numerical results except around the end of inflation. Due to the presence of isocurvature perturbations, the gravitational potential $Φ$ and the curvature perturbations ${\cal R}$ and $ζ$ do not remain constant on super-horizon scales. In particular, we find that negative non-minimal coupling can lead to strong enhancement of ${\cal R}$ in both the Einstein and higher derivative gravity, in which case it is difficult to unambiguously decompose scalar perturbations into adiabatic and isocurvature modes during the whole stage of inflation.

astro-ph↗

arXiv1998

Sine-Gordon Parametric Resonance

We consider the instability of fluctuations in an oscillating scalar field which obeys the Sine-Gordon equation. We present simple closed-form analytic solutions describing the parametric resonance in the Sine-Gordon model. The structure of the resonance differs from that obtained with the Mathieu equation which is usually derived with the small angle approximation to the equation for fluctuations. The results are applied to axion cosmology, where the oscillations of the classical axion field, with a Sine-Gordon self-interaction potential, constitute the cold dark matter of the universe. When the axion misalignment angle at the QCD epoch, $θ_0$, is small, the parametric resonance of the axion fluctuations is not significant. However, in regions of larger $θ_0$ where axion miniclusters would form, the resonance may be important. As a result, axion miniclusters may disintegrate into finer, denser clumps. We also apply the theory of Sine-Gordon parametric resonance to reheating in the Natural Inflation scenario. The decay of the inflaton field due to the self-interaction alone is ineffective, but a coupling to other bosons can lead to preheating in the broad resonance regime. Together with the preheating of fermions, this can alter the reheating scenario for Natural Inflation.

hep-ph↗

arXiv1998

On the Phase-Space Volume of Primordial Cosmological Perturbations

We show how to determine the typical phase space volume $Γ$ for primordial gravitational waves produced during an inflationary stage, which is invariant under squeezing. An expression for $Γ$ is found in the long wavelength regime. The quasi-classical entropy of a pure vacuum initial state defined as the logarithm of $Γ$ modulo a constant remains zero in spite of the generation of fluctuations (creation of real gravitons).

gr-qc↗

arXiv1998

The Coherence of Primordial Fluctuations Produced During Inflation

The behaviour of quantum metric perturbations produced during inflation is considered at the stage after the second Hubble radius crossing. It is shown that the classical correlation between amplitude and momentum of a perturbation mode, previously shown to emerge in the course of an effective quantum-to-classical transition, is maintained for a sufficiently long time, and we present the explicit form in which it takes place using the Wigner function. We further show with a simple diffraction experiment that quantum interference, non-expressible in terms of a classical stochastic description of the perturbations, is essentially suppressed. Rescattering of the perturbations leads to a comparatively slow decay of this correlation and to a complete stochastization of the system.

gr-qc↗

arXiv1997

Constraining topology with the CMB

We present a new data analysis method to study rectangular T^3 ``small universes" with one or two of its dimensions significantly smaller than the present horizon (which we refer to as T^1- and T^2-models, respectively). We find that the 4 year COBE/DMR data set a lower limit on the smallest cell size for T^1- and T^2-models of 3000h^{-1} Mpc, at 95% confidence, for a scale invariant power spectrum (n=1).

astro-ph↗

arXiv1997

Can the lack of symmetry in the COBE/DMR maps constrain the topology of the universe?

Although the cubic T^3 "small universe" has been ruled out by COBE/DMR results as an interesting cosmological model, we still have the possibility of living in a universe with a more anisotropic topology such as a rectangular T^3 "small universe" with one or two of its dimensions significantly smaller than the present horizon (which we refer to as T^1- and T^2-models, respectively). In order to rule out these anisotropic topologies as well, we apply a new data analysis method that searches for the specific kind of symmetries that these models should produce. We find that the 4 year COBE/DMR data set a lower limit on the smallest cell size for T^1- and T^2-models of 3000h^{-1} Mpc, at 95% confidence, for a scale invariant power spectrum (n=1). These results imply that ALL toroidal universes (cubes and rectangles) are ruled out as interesting cosmological models.

astro-ph↗

arXiv1996

Quantum-to-classical Transition of Cosmological Perturbations for Non-vacuum Initial States

Transition from quantum to semiclassical behaviour and loss of quantum coherence for inhomogeneous perturbations generated from a non-vacuum initial state in the early Universe is considered in the Heisenberg and the Schrödinger representations, as well as using the Wigner function. We show explicitly that these three approaches lead to the same prediction in the limit of large squeezing (i.e. when the squeezing parameter $|r_k|\to \infty$): each two-modes quantum state (k, -k) of these perturbations is equivalent to a classical perturbation that has a stochastic amplitude, obeying a non-gaussian statistics which depends on the initial state, and that belongs to the quasi-isotropic mode (i.e. it possesses a fixed phase). The Wigner function is not everywhere positive for any finite $r_k$, hence its interpretation as a classical distribution function in phase space is impossible without some coarse graining procedure. However, this does not affect the transition to semiclassical behaviour since the Wigner function becomes concentrated near a classical trajectory in phase space when $|r_k|\to \infty$ even without coarse graining. Deviations of the statistics of the perturbations in real space from a Gaussian one lie below the cosmic variance level for the N-particles initial states with N=N(|k|) but may be observable for other initial states without statistical isotropy or with correlations between different k modes. As a way to look for this effect, it is proposed to measure the kurtosis of the angular fluctuations of the cosmic microwave background temperature.

gr-qc↗

arXiv1996

Semiclassicality and Decoherence of Cosmological Perturbations

Transition to the semiclassical behaviour and the decoherence process for inhomogeneous perturbations generated from the vacuum state during an inflationary stage in the early Universe are considered both in the Heisenberg and the Schrödinger representations to show explicitly that both approaches lead to the same prediction: the equivalence of these quantum perturbations to classical perturbations having stochastic Gaussian amplitudes and belonging to the quasi-isotropic mode. This equivalence and the decoherence are achieved once the exponentially small (in terms of the squeezing parameter $r_k$) decaying mode is neglected. In the quasi-classical limit $|r_k|\to \infty$, the perturbation mode functions can be made real by a time-independent phase rotation, this is shown to be equivalent to a fixed relation between squeezing angle and phase for all modes in the squeezed-state formalism. Though the present state of the gravitational wave background is not a squeezed quantum state in the rigid sense and the squeezing parameters loose their direct meaning due to interaction with the environment and other processes, the standard predictions for the rms values of the perturbations generated during inflation are not affected by these mechanisms (at least, for scales of interest in cosmological applications). This stochastic background still occupies a small part of phase space.

gr-qc↗

arXiv1996

Non-Thermal Phase Transitions after Inflation

At the first stage of reheating after inflation, parametric resonance may rapidly transfer most of the energy of an inflaton field $ϕ$ to the energy of other bosons. We show that quantum fluctuations of scalar and vector fields produced at this stage are much greater than they would be in a state of thermal equilibrium. This leads to cosmological phase transitions of a new type, which may result in a copious production of topological defects and in a secondary stage of inflation after reheating.

hep-th↗

arXiv1995

Skewness of Cosmic Microwave Background Temperature Fluctuations Due to Non-linear Gravitational Instability

Skewness of temperature fluctuations of the cosmic microwave background (CMB) produced by initially Gaussian adiabatic perturbations with the flat (Harrison-Zeldovich) spectrum, which arises due to non-linear corrections to a gravitational potential at the matter-dominated stage, is calculated quantitatively. For the standard CDM model, the effect appears to be smaller than expected previously and lies below the cosmic variance limit even for small angles. The sign of the skewness is opposite to that of the skewness of density perturbations.

astro-ph↗

arXiv1995

Structure of Primordial Gravitational Waves Spectrum in a Double Inflationary Model

The gravitational waves (GW) background generated in a double inflationary model, with two scalar fields mutually interacting through gravity only, and its relative contribution $T/S$ to large-angle temperature fluctuations of the relic microwave background are investigated in detail. The relation between $T/S$ and the slope of the GW spectrum $n_T$ is shown to be a discriminative test between a slow-roll inflation driven by one scalar field and more complicated models. It is found that the GW amplitude is not exactly zero in minima of spectral oscillations, this property being an observational, in principle, manifestation of GW being in a squeezed vacuum state during inflation.

astro-ph↗

arXiv1995

Density fluctuations in Brans-Dicke inflation

Spectrum of density perturbations in the Universe generated from quantum-gravitational fluctuations in slow-roll-over inflationary scenarios with the Brans-Dicke gravity is calculated. It is shown that after inflation the isocurvature mode of perturbations may be neglected as compared to the adiabatic mode, and that an amplitude of the latter mode is not significantly different from that in the Einstein gravity. However, the account of the isocurvature mode is necessary to obtain the quantitatively correct spectrum of adiabatic perturbations.

gr-qc↗