arXiv subjects

Alexander Vilenkin

Publications and source records attributed to Alexander Vilenkin.

At least 37 records · Page 2Linked to original sources

arXiv2019

Tunneling wave function of the universe II: the backreaction problem

The tunneling wave function of the universe is calculated exactly for a de Sitter minisuperspace model with a massless conformally coupled scalar field, both by solving the Wheeler-DeWitt equation and by evaluating the Lorentzian path integral. The same wave function is found in both approaches. The back-reaction of quantum field fluctuations on the scale factor amounts to a constant renormalization of the vacuum energy density. This is in contrast to the recent suggestion of Feldbrugge $et$ $al.$ that the back-reaction should diverge when the scale factor gets small, $a \to 0$. Similar results are found for a massive scalar field in the limit of a large mass. We also verified that the tunneling wave function can be expressed as a transition amplitude from a universe of vanishing size with the scalar field in the state of Euclidean vacuum, as it was suggested in our earlier work.

gr-qc↗

arXiv2018

Tunneling wave function of the universe

The tunneling wave function of the universe is investigated in a minisuperspace framework of a de Sitter universe with a quantum scalar field, treated as a perturbation. We consider three different approaches to defining the tunneling wave function: (1) tunneling boundary conditions in superspace, (2) Lorentzian path integral, and (3) quantum tunneling from initial universe of a vanishing size. We show that the superspace approach requires Robin boundary conditions for the scalar field modes, the path integral approach requires adding an appropriate boundary term to the scalar field action, and the initial universe approach requires the initial quantum state of the scalar field to be Euclidean vacuum. We find that all three approaches yield identical wave functions and that scalar field fluctuations are well behaved, contrary to earlier claims in the literature.

gr-qc↗

arXiv2018

Inflation in Random Landscapes with two energy scales

We investigate inflation in a multi-dimensional landscape with a hierarchy of energy scales, motivated by the string theory, where the energy scale of Kahler moduli is usually assumed to be much lower than that of complex structure moduli and dilaton field. We argue that in such a landscape, the dynamics of slow-roll inflation is governed by the low-energy potential, while the initial condition for inflation are determined by tunneling through high-energy barriers. We then use the scale factor cutoff measure to calculate the probability distribution for the number of inflationary e-folds and the amplitude of density fluctuations $Q$, assuming that the low-energy landscape is described by a random Gaussian potential with a correlation length much smaller than $M_{\rm pl}$. We find that the distribution for $Q$ has a unique shape and a preferred domain, which depends on the parameters of the low-energy landscape. We discuss some observational implications of this distribution and the constraints it imposes on the landscape parameters.

hep-th↗

arXiv2018

Cosmic strings and primordial black holes

Cosmic strings and primordial black holes (PBHs) commonly and naturally form in many scenarios describing the early universe. Here we show that if both cosmic strings and PBHs are present, their interaction leads to a range of interesting consequences. At the time of their formation, the PBHs get attached to the strings and influence their evolution, leading to the formation of black-hole-string networks and commonly to the suppression of loop production in a range of redshifts. Subsequently, reconnections within the network give rise to small nets made of several black holes and connecting strings. The number of black holes in the network as well as the stability of the nets depend on the topological properties of the strings. The nets oscillate and shrink exponentially due to the emission of gravitational waves. This leads to potentially observable string-driven mergers of PBHs. The strings can keep PBHs from galactic halos, making the current bounds on PBHs not generally applicable. Alternatively, heavy PBHs can drag low-tension strings into the centers of galaxies. The superconducting strings can appear as radio filaments pointing towards supermassive black holes.

astro-ph.CO↗

arXiv2018

CMB spectral distortions from black holes formed by vacuum bubbles

Vacuum bubbles may nucleate and expand during the cosmic inflation. When inflation ends, the bubbles run into the ambient plasma, producing strong shocks followed by underdensity waves, which propagate outwards. The bubbles themselves eventually form black holes with a wide distribution of masses. It has been recently suggested that such black holes may account for LIGO observations and may provide seeds for supermassive black holes observed at galactic centers. They may also provide a significant part or even the whole of the dark matter. We estimate the spectral $μ$-distortion of the CMB induced by expanding shocks and underdensities. The predicted distortions averaged over the sky are well below the current bounds, but localized peaks due to the largest black holes impose constraints on the model parameters.

gr-qc↗

arXiv2018

Primordial black hole formation by vacuum bubbles

Vacuum bubbles may nucleate during the inflationary epoch and expand, reaching relativistic speeds. After inflation ends, the bubbles are quickly slowed down, transferring their momentum to a shock wave that propagates outwards in the radiation background. The ultimate fate of the bubble depends on its size. Bubbles smaller than certain critical size collapse to ordinary black holes, while in the supercritical case the bubble interior inflates, forming a baby universe, which is connected to the exterior region by a wormhole. The wormhole then closes up, turning into two black holes at its two mouths. We use numerical simulations to find the masses of black holes formed in this scenario, both in subcritical and supercritical regime. The resulting mass spectrum is extremely broad, ranging over many orders of magnitude. For some parameter values, these black holes can serve as seeds for supermassive black holes and may account for LIGO observations.

gr-qc↗

arXiv2018

Inflation in multi-field random Gaussian landscapes

We investigate slow-roll inflation in a multi-field random Gaussian landscape. The landscape is assumed to be small-field, with a correlation length much smaller than the Planck scale. Inflation then typically occurs in small patches of the landscape, localized near inflection or saddle points. We find that the inflationary track is typically close to a straight line in the field space, and the statistical properties of inflation are similar to those in a one-dimensional landscape. This picture of multi-field inflation is rather different from that suggested by the Dyson Brownian motion model; we discuss the reasons for this difference. We also discuss tunneling from inflating false vacua to the neighborhood of inflection and saddle points and show that the tunneling endpoints tend to concentrate along the flat direction in the landscape.

hep-th↗

arXiv2017

Hessian eigenvalue distribution in a random Gaussian landscape

The energy landscape of multiverse cosmology is often modeled by a multi-dimensional random Gaussian potential. The physical predictions of such models crucially depend on the eigenvalue distribution of the Hessian matrix at potential minima. In particular, the stability of vacua and the dynamics of slow-roll inflation are sensitive to the magnitude of the smallest eigenvalues. The Hessian eigenvalue distribution has been studied earlier, using the saddle point approximation, in the leading order of $1/N$ expansion, where $N$ is the dimensionality of the landscape. This approximation, however, is insufficient for the small eigenvalue end of the spectrum, where sub-leading terms play a significant role. We extend the saddle point method to account for the sub-leading contributions. We also develop a new approach, where the eigenvalue distribution is found as an equilibrium distribution at the endpoint of a stochastic process (Dyson Brownian motion). The results of the two approaches are consistent in cases where both methods are applicable. We discuss the implications of our results for vacuum stability and slow-roll inflation in the landscape.

hep-th↗

arXiv2017

Initial conditions for slow-roll inflation in a random Gaussian landscape

In the landscape perspective, our Universe begins with a quantum tunneling from an eternally-inflating parent vacuum, followed by a period of slow-roll inflation. We investigate the tunneling process and calculate the probability distribution for the initial conditions and for the number of e-folds of slow-roll inflation, modeling the landscape by a small-field one-dimensional random Gaussian potential. We find that such a landscape is fully consistent with observations, but the probability for future detection of spatial curvature is rather low, $P \sim 10^{-3}$.

hep-th↗

arXiv2017

Primordial black hole and wormhole formation by domain walls

In theories with a broken discrete symmetry, Hubble sized spherical domain walls may spontaneously nucleate during inflation. These objects are subsequently stretched by the inflationary expansion, resulting in a broad distribution of sizes. The fate of the walls after inflation depends on their radius. Walls smaller than a critical radius fall within the cosmological horizon early on and collapse due to their own tension, forming ordinary black holes. But if a wall is large enough, its repulsive gravitational field becomes dominant much before the wall can fall within the cosmological horizon. In this "supercritical" case, a wormhole throat develops, connecting the ambient exterior FRW universe with an interior baby universe, where the exponential growth of the wall radius takes place. The wormhole pinches off in a time-scale comparable to its light-crossing time, and black holes are formed at its two mouths. As discussed in previous work, the resulting black hole population has a wide distribution of masses and can have significant astrophysical effects. The mechanism of black hole formation has been previously studied for a dust-dominated universe. Here we investigate the case of a radiation-dominated universe, which is more relevant cosmologically, by using numerical simulations in order to find the initial mass of a black hole as a function of the wall size at the end of inflation. For large supercritical domain walls, this mass nearly saturates the upper bound according to which the black hole cannot be larger than the cosmological horizon. We also find that the subsequent accretion of radiation satisfies a scaling relation, resulting in a mass increase by about a factor of 2.

gr-qc↗

arXiv2017

Inflation in random Gaussian landscapes

We develop analytic and numerical techniques for studying the statistics of slow-roll inflation in random Gaussian landscapes. As an illustration of these techniques, we analyze small-field inflation in a one-dimensional landscape. We calculate the probability distributions for the maximal number of e-folds and for the spectral index of density fluctuations $n_s$ and its running $α_s$. These distributions have a universal form, insensitive to the correlation function of the Gaussian ensemble. We outline possible extensions of our methods to a large number of fields and to models of large-field inflation. These methods do not suffer from potential inconsistencies inherent in the Brownian motion technique, which has been used in most of the earlier treatments.

hep-th↗

arXiv2016

Fireballs from Superconducting Cosmic Strings

Thermalized fireballs should be created by cusp events on superconducting cosmic strings. This simple notion allows to reliably estimate particle emission from the cusps in a given background magnetic field. With plausible assumptions about intergalactic magnetic fields, the cusp events can produce observable fluxes of high-energy photons and neutrinos with unique signatures.

astro-ph.HE↗

arXiv2016

Black holes and the multiverse

Vacuum bubbles may nucleate and expand during the inflationary epoch in the early universe. After inflation ends, the bubbles quickly dissipate their kinetic energy; they come to rest with respect to the Hubble flow and eventually form black holes. The fate of the bubble itself depends on the resulting black hole mass. If the mass is smaller than a certain critical value, the bubble collapses to a singularity. Otherwise, the bubble interior inflates, forming a baby universe, which is connected to the exterior FRW region by a wormhole. A similar black hole formation mechanism operates for spherical domain walls nucleating during inflation. As an illustrative example, we studied the black hole mass spectrum in the domain wall scenario, assuming that domain walls interact with matter only gravitationally. Our results indicate that, depending on the model parameters, black holes produced in this scenario can have significant astrophysical effects and can even serve as dark matter or as seeds for supermassive black holes. The mechanism of black hole formation described in this paper is very generic and has important implications for the global structure of the universe. Baby universes inside super-critical black holes inflate eternally and nucleate bubbles of all vacua allowed by the underlying particle physics. The resulting multiverse has a very non-trivial spacetime structure, with a multitude of eternally inflating regions connected by wormholes. If a black hole population with the predicted mass spectrum is discovered, it could be regarded as evidence for inflation and for the existence of a multiverse.

hep-th↗

arXiv2016

Vacuum statistics and stability in axionic landscapes

We investigate vacuum statistics and stability in random axionic landscapes. For this purpose we developed an algorithm for a quick evaluation of the tunneling action, which in most cases is accurate within 10%. We find that stability of a vacuum is strongly correlated with its energy density, with lifetime rapidly growing as the energy density is decreased. The probability $P(B)$ for a vacuum to have a tunneling action $B$ greater than a given value declines as a slow power law in $B$. This is in sharp contrast with the studies of random quartic potentials, which found a fast exponential decline of $P(B)$. Our results suggest that the total number of relatively stable vacua (say, with $B> 100$) grows exponentially with the number of fields $N$ and can get extremely large for $N\gtrsim 100$. The problem with this kind of model is that the stable vacua are concentrated near the absolute minimum of the potential, so the observed value of the cosmological constant cannot be explained without fine-tuning. To address this difficulty, we consider a modification of the model, where the axions acquire a quadratic mass term, due to their mixing with 4-form fields. This results in a larger landscape with a much broader distribution of vacuum energies. The number of relatively stable vacua in such models can still be extremely large.

gr-qc↗

arXiv2015

Tunneling decay rate in quantum cosmology

In canonical quantum cosmology, the wave function of the universe lacks explicit time dependence. However, time evolution may be present implicitly through the semiclassical superspace variables, which themselves depend on time in classical dynamics. In this paper, we apply this approach to an oscillating universe model recently introduced by Graham et al. By extending the model to include a massless, minimally coupled scalar field $ϕ$ which has little effect on the dynamics but can play the role of a "clock", we determine the decay rate of the oscillating universe.

hep-th↗

arXiv2015

Topological Defects from the Multiverse

Many theories of the early universe predict the existence of a multiverse where bubbles continuously nucleate giving rise to observers in their interior. In this paper, we point out that topological defects of several dimensionalities will also be produced in de Sitter like regions of the multiverse. In particular, defects could be spontaneously nucleated in our parent vacuum. We study the evolution of these defects as they collide with and propagate inside of our bubble. We estimate the present distribution of defects in the observable part of the universe. The expected number of such nearby defects turns out to be quite small, even for the highest nucleation rate. We also study collisions of strings and domain walls with our bubble in our past light cone. We obtain simulated full-sky maps of the loci of such collisions, and find their angular size distribution. Similarly to what happens in the case of bubble collisions, the prospect of detecting any collisions of our bubble with ambient defects is greatly enhanced in the case where the cosmological constant of our parent vacuum is much higher than the vacuum energy density during inflation in our bubble.

hep-th↗

arXiv2014

Stablizing oscillating universes against quantum decay

We investigate the effect of vacuum corrections, due to the trace anomaly and Casimir effect, on the stability of an oscillating universe with respect to decay by tunneling to the singularity. We find that these corrections do not generally stabilize an oscillating universe. However, stability may be achieved for some specially fine-tuned non-vacuum states.

hep-th↗

arXiv2014

Instability of an emergent universe

Oscillating solutions to the effective equations of Loop Quantum Cosmology have been suggested for the role of an `eternal seed', providing a possible starting point for the emergent universe scenario. We investigate the stability of a particular model, sourced by a homogeneous massless scalar field and a negative cosmological constant, with respect to small perturbations and to quantum collapse. We find that the model has perturbatively stable and unstable solutions, with both types of solutions occupying significant regions of the parameter space. All solutions are unstable with respect to collapse by quantum tunneling to zero size. We discuss the possibility that the state resulting from the collapse is non-singular, so it may tunnel back to the oscillating regime. We argue that the universe is then likely to evolve to states of very large size with large particle occupation numbers.

hep-th↗