arXiv subjects

Neil Turok

Publications and source records attributed to Neil Turok.

At least 73 records · Page 4Linked to original sources

arXiv2006

Cosmic Perturbations Through the Cyclic Ages

We analyze the evolution of cosmological perturbations in the cyclic model, paying particular attention to their behavior and interplay over multiple cycles. Our key results are: (1) galaxies and large scale structure present in one cycle are generated by the quantum fluctuations in the preceding cycle without interference from perturbations or structure generated in earlier cycles and without interfering with structure generated in later cycles; (2) the ekpyrotic phase, an epoch of gentle contraction with equation of state $w\gg 1$ preceding the hot big bang, makes the universe homogeneous, isotropic and flat within any given observer's horizon; and, (3) although the universe is uniform within each observer's horizon, the global structure of the cyclic universe is more complex, owing to the effects of superhorizon length perturbations, and cannot be described in a uniform Friedmann-Robertson-Walker picture. In particular, we show that the ekpyrotic phase is so effective in smoothing, flattening and isotropizing the universe within the horizon that this phase alone suffices to solve the horizon and flatness problems even without an extended period of dark energy domination (a kind of low energy inflation). Instead, the cyclic model rests on a genuinely novel, non-inflationary mechanism (ekpyrotic contraction) for resolving the classic cosmological conundrums.

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arXiv2006

Why the cosmological constant is small and positive

Within conventional big bang cosmology, it has proven to be very difficult to understand why today's cosmological constant is so small. In this paper, we show that a cyclic model of the universe can naturally incorporate a dynamical mechanism that automatically relaxes the value of the cosmological constant, taking account of contributions to the vacuum density at all energy scales. Because the relaxation time grows exponentially as the vacuum density decreases, nearly every volume of space spends an overwhelming majority of the time at the stage when the cosmological constant is small and positive, as observed today.

astro-ph↗

arXiv2006

Inflationary predictions for scalar and tensor fluctuations reconsidered

We reconsider the predictions of inflation for the spectral index of scalar (energy density) fluctuations (n_s) and the tensor/scalar ratio (r) using a discrete, model-independent measure of the degree of fine-tuning required to obtain a given combination of (n_s, r). We find that, except for cases with numerous unnecessary degrees of fine-tuning, n_s is less than 0.98, measurably different from exact Harrison-Zel'dovich. Furthermore, if n_s \gtrsim 0.95, in accord with current measurements, the tensor/scalar ratio satisfies r \gtrsim 10^{-2}, a range that should be detectable in proposed cosmic microwave background polarization experiments and direct gravitational wave searches.

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arXiv2006

Solution of a Braneworld Big Crunch/Big Bang Cosmology

We solve for the cosmological perturbations in a five-dimensional background consisting of two separating or colliding boundary branes, as an expansion in the collision speed V divided by the speed of light c. Our solution permits a detailed check of the validity of four-dimensional effective theory in the vicinity of the event corresponding to the big crunch/big bang singularity. We show that the four-dimensional description fails at the first nontrivial order in (V/c)^2. At this order, there is nontrivial mixing of the two relevant four-dimensional perturbation modes (the growing and decaying modes) as the boundary branes move from the narrowly-separated limit described by Kaluza-Klein theory to the well-separated limit where gravity is confined to the positive-tension brane. We comment on the cosmological significance of the result and compute other quantities of interest in five-dimensional cosmological scenarios.

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arXiv2006

Classical Propagation of Strings across a Big Crunch/Big Bang Singularity

One of the simplest time-dependent solutions of M theory consists of nine-dimensional Euclidean space times 1+1-dimensional compactified Milne space-time. With a further modding out by Z_2, the space-time represents two orbifold planes which collide and re-emerge, a process proposed as an explanation of the hot big bang. When the two planes are near, the light states of the theory consist of winding M2-branes, describing fundamental strings in a particular ten-dimensional background. They suffer no blue-shift as the M theory dimension collapses, and their equations of motion are regular across the transition from big crunch to big bang. In this paper, we study the classical evolution of fundamental strings across the singularity in some detail. We also develop a simple semi-classical approximation to the quantum evolution which allows one to compute the quantum production of excitations on the string and implement it in a simplified example.

hep-th↗

arXiv2005

Controlling Chaos through Compactification in Cosmological Models with a Collapsing Phase

We consider the effect of compactification of extra dimensions on the onset of classical chaotic "Mixmaster" behavior during cosmic contraction. Assuming a universe that is well-approximated as a four-dimensional Friedmann-Robertson--Walker model (with negligible Kaluza-Klein excitations) when the contraction phase begins, we identify compactifications that allow a smooth contraction and delay the onset of chaos until arbitrarily close the big crunch. These compactifications are defined by the de Rham cohomology (Betti numbers) and Killing vectors of the compactification manifold. We find compactifications that control chaos in vacuum Einstein gravity, as well as in string theories with N = 1 supersymmetry and M-theory. In models where chaos is controlled in this way, the universe can remain homogeneous and flat until it enters the quantum gravity regime. At this point, the classical equations leading to chaotic behavior can no longer be trusted, and quantum effects may allow a smooth approach to the big crunch and transition into a subsequent expanding phase. Our results may be useful for constructing cosmological models with contracting phases, such as the ekpyrotic/cyclic and pre-big bang models.

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arXiv2005

Langevin Analysis of Eternal Inflation

It has been widely claimed that inflation is generically eternal to the future, even in models where the inflaton potential monotonically increases away from its minimum. The idea is that quantum fluctuations allow the field to jump uphill, thereby continually revitalizing the inflationary process in some regions. In this paper we investigate a simple model of this process, pertaining to inflation with a quartic potential, in which analytic progress may be made. We calculate several quantities of interest, such as the expected number of inflationary efolds, first without and then with various selection effects. With no additional weighting, the stochastic noise has little impact on the total number of inflationary efoldings even if the inflaton starts with a Planckian energy density. A "rolling" volume factor, i.e. weighting in proportion to the volume at that time, also leads to a monotonically decreasing Hubble constant and hence no eternal inflation. We show how stronger selection effects including a constraint on the initial and final states and weighting with the final volume factor can lead to a picture similar to that usually associated with eternal inflation.

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arXiv2005

Conformal symmetry of brane world effective actions

A simple derivation of the low-energy effective action for brane worlds is given, highlighting the role of conformal invariance. We show how to improve the effective action for a positive- and negative-tension brane pair using the AdS/CFT correspondence.

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arXiv2004

Effective theory approach to brane world black holes

We derive static spherically-symmetric vacuum solutions of the low-energy effective action for the two brane Randall-Sundrum model. The solutions with non-trivial radion belong to a one-parameter family describing traversable wormholes between the branes and a black hole, and were first discovered in the context of Einstein gravity with a conformally-coupled scalar field. From a brane world perspective, a distinctive feature of all the solutions with non-trivial radion is a brane intersection about which the bulk geometry is conical but the induced metrics on the branes are regular. Contrary to earlier claims in the literature, we show these solutions are stable under monopole perturbations.

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arXiv2004

M Theory Model of a Big Crunch/Big Bang Transition

We consider a picture in which the transition from a big crunch to a big bang corresponds to the collision of two empty orbifold planes approaching each other at a constant non-relativistic speed in a locally flat background space-time, a situation relevant to recently proposed cosmological models. We show that $p$-brane states which wind around the extra dimension propagate smoothly and unambiguously across the orbifold plane collision. In particular we calculate the quantum mechanical production of winding M2-branes extending from one orbifold to the other. We find that the resulting density is finite and that the resulting gravitational back-reaction is small. These winding states, which include the string theory graviton, can be propagated smoothly across the transition using a perturbative expansion in the membrane tension, an expansion which from the point of view of string theory is an expansion in {\it inverse} powers of $α'$. We argue that interactions should be well-behaved because the string coupling tends to zero at the crunch. The production of massive Kaluza-Klein states should also be exponentially suppressed for small collision speeds. We contrast this good behavior with that found in previous studies of strings in Lorentzian orbifolds.

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arXiv2004

The Cyclic Model Simplified

The Cyclic Model attempts to resolve the homogeneity, isotropy, and flatness problems and generate a nearly scale-invariant spectrum of fluctuations during a period of slow contraction that precedes a bounce to an expanding phase. Here we describe at a conceptual level the recent developments that have greatly simplified our understanding of the contraction phase and the Cyclic Model overall. The answers to many past questions and criticisms are now understood. In particular, we show that the contraction phase has equation of state w>1 and that contraction with w>1 has a surprisingly similar properties to inflation with w < -1/3. At one stroke, this shows how the model is different from inflation and why it may work just as well as inflation in resolving cosmological problems.

astro-ph↗

arXiv2004

The shapes of dark matter dominated dwarf spheroidal stellar density profiles

A Bayesian likelihood analysis of the stellar density profile shapes of several dark matter dominated Galactic dwarf spheroidal galaxies (dSphs) has been completed. This analysis indicates that the inner power law, ρ\propto r^{-γ}, of each of these profiles satisfies γ< 1.21 at greater than 99% confidence with a slight preference for γ\sim 0.7 . Speculating that this bound on the stellar profiles may be related to the inner power law of the underlying dark matter distribution reveals a statistical discrepancy with the values favoured by recent N-body simulations of cold dark matter (CDM), γ_{CDM} \sim 1.4-1.5 .

astro-ph↗

arXiv2004

Kasner and Mixmaster behavior in universes with equation of state w \ge 1

We consider cosmological models with a scalar field with equation of state $w\ge 1$ that contract towards a big crunch singularity, as in recent cyclic and ekpyrotic scenarios. We show that chaotic mixmaster oscillations due to anisotropy and curvature are suppressed, and the contraction is described by a homogeneous and isotropic Friedmann equation if $w>1$. We generalize the results to theories where the scalar field couples to p-forms and show that there exists a finite value of $w$, depending on the p-forms, such that chaotic oscillations are suppressed. We show that $Z_2$ orbifold compactification also contributes to suppressing chaotic behavior. In particular, chaos is avoided in contracting heterotic M-theory models if $w>1$ at the crunch.

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arXiv2004

A new duality relating density perturbations in expanding and contracting Friedmann cosmologies

For a 4-dimensional spatially-flat Friedmann-Robertson-Walker universe with a scalar field $ϕ(x)$, potential $V(ϕ)$ and constant equation of state $w=p/ρ$, we show that an expanding solution characterized by $ε=3(1+w)/2$ produces the same scalar perturbations as a contracting solution with $\hatε=1/ε$. The same symmetry applies to both the dominant and subdominant scalar perturbation modes. This result admits a simple physical interpretation and generalizes to $d$ spacetime dimensions if we define $ε\equiv [(2d-5)+(d-1)w]/(d-2)$.

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arXiv2004

Beyond Inflation: A Cyclic Universe Scenario

Inflation has been the leading early universe scenario for two decades, and has become an accepted element of the successful `cosmic concordance' model. However, there are many puzzling features of the resulting theory. It requires both high energy and low energy inflation, with energy densities differing by a hundred orders of magnitude. The questions of why the universe started out undergoing high energy inflation, and why it will end up in low energy inflation, are unanswered. Rather than resort to anthropic arguments, we have developed an alternative cosmology, the Cyclic universe, in which the universe exists in a very long-lived attractor state determined by the laws of physics. The model shares inflation's phenomenological successes without requiring an epoch of high energy inflation. Instead, the universe is made homogeneous and flat, and scale-invariant adiabatic perturbations are generated during an epoch of low energy acceleration like that seen today, but preceding the last big bang. Unlike inflation, the model requires low energy acceleration in order for a periodic attractor state to exist. The key challenge facing the scenario is that of passing through the cosmic singularity at t=0. Substantial progress has been made at the level of linearised gravity, which is reviewed here. The challenge of extending this to nonlinear gravity and string theory remains.

hep-th↗

arXiv2004

Designing Cyclic Universe Models

Recent advances in understanding the propagation of perturbations through the transition from big crunch to big bang (esp. Tolley et al. hep-th/0306109) make it possible for the first time to consider the full set of phenomenological constraints on the scalar field potential in cyclic models of the universe. We show that cyclic models require a comparable degree of tuning to that needed for inflationary models. The constraints are reduced to a set of simple design rules including "fast-roll" parameters analogous to the "slow-roll" parameters in inflation.

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arXiv2003

Inflation versus Cyclic Predictions for Spectral Tilt

We present a simple, nearly model-independent estimate that yields the predictions of the simplest inflationary and ekpyrotic/cyclic models for the spectral tilt of the primordial density inhomogeneities. Remarkably, we find that the simplest models yield an identical result: n_s is approximately 0.95. For inflation, the same estimate predicts a ratio of tensor to scalar contributions to the low multipoles of the microwave background anisotropy of T/S=20%; the tensor contribution is negligible for ekpyrotic/cyclic models.

astro-ph↗

arXiv2003

The cosmic gravitational wave background in a cyclic universe

Inflation predicts a primordial gravitational wave spectrum that is slightly ``red,'' i.e., nearly scale-invariant with slowly increasing power at longer wavelengths. In this paper, we compute both the amplitude and spectral form of the primordial tensor spectrum predicted by cyclic/ekpyrotic models. The spectrum is blue and exponentially suppressed compared to inflation on long wavelengths. The strongest observational constraint emerges from the requirement that the energy density in gravitational waves should not exceed around 10 per cent of the energy density at the time of nucleosynthesis.

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