arXiv subjects

Alexander Westphal

Publications and source records attributed to Alexander Westphal.

At least 55 records · Page 3Linked to original sources

arXiv2017

Inflation with a graceful exit in a random landscape

We develop a stochastic description of small-field inflationary histories with a graceful exit in a random potential whose Hessian is a Gaussian random matrix as a model of the unstructured part of the string landscape. The dynamical evolution in such a random potential from a small-field inflation region towards a viable late-time de Sitter (dS) minimum maps to the dynamics of Dyson Brownian motion describing the relaxation of non-equilibrium eigenvalue spectra in random matrix theory. We analytically compute the relaxation probability in a saddle point approximation of the partition function of the eigenvalue distribution of the Wigner ensemble describing the mass matrices of the critical points. When applied to small-field inflation in the landscape, this leads to an exponentially strong bias against small-field ranges and an upper bound $N\ll 10$ on the number of light fields $N$ participating during inflation from the non-observation of negative spatial curvature.

hep-th↗

arXiv2016

Towards Axion Monodromy Inflation with Warped KK-Modes

We present a particularly simple model of axion monodromy: Our axion is the lowest-lying KK-mode of the RR-2-form-potential $C_2$ in the standard Klebanov-Strassler throat. One can think of this inflaton candidate as being defined by the integral of $C_2$ over the $S^2$ cycle of the throat. It obtains an exponentially small mass from the IR-region in which the $S^2$ shrinks to zero size both with respect to the Planck scale and the mass scale of local modes of the throat. Crucially, the $S^2$ cycle has to be shared between two throats, such that the second locus where the $S^2$ shrinks is also in a warped region. Well-known problems like the potentially dangerous back-reaction of brane/antibrane pairs and explicit supersymmetry breaking are not present in our scenario. However, the inflaton back-reaction starts to deform the geometry strongly once the field excursion approaches the Planck scale. We derive the system of differential equations required to treat this effect quantitatively. Numerical work is required to decide whether back-reaction makes the model suitable for realistic inflation. While we have to leave this crucial issue to future studies, we find it interesting that such a simple and explicit stringy monodromy model allows an originally sub-Planckian axion to go through many periods with full quantitative control before back-reaction becomes strong. Also, the mere existence of our ultra-light throat mode (with double exponentially suppressed mass) is noteworthy.

hep-th↗

arXiv2016

Runaway Relaxion Monodromy

We examine the relaxion mechanism in string theory. An essential feature is that an axion winds over $N \gg 1$ fundamental periods. In string theory realizations via axion monodromy, this winding number corresponds to a physical charge carried by branes or fluxes. We show that this monodromy charge backreacts on the compact space, ruining the structure of the relaxion action. In particular, the barriers generated by strong gauge dynamics have height $\propto e^{-N}$, so the relaxion does not stop when the Higgs acquires a vev. Backreaction of monodromy charge can therefore spoil the relaxion mechanism. We comment on the limitations of technical naturalness arguments in this context.

hep-th↗

arXiv2016

Axion Monodromy and the Weak Gravity Conjecture

Axions with broken discrete shift symmetry (axion monodromy) have recently played a central role both in the discussion of inflation and the `relaxion' approach to the hierarchy problem. We suggest a very minimalist way to constrain such models by the weak gravity conjecture for domain walls: While the electric side of the conjecture is always satisfied if the cosine-oscillations of the axion potential are sufficiently small, the magnetic side imposes a cutoff, $Λ^3 \sim m f M_{pl}$, independent of the height of these `wiggles'. We compare our approach with the recent related proposal by Ibanez, Montero, Uranga and Valenzuela. We also discuss the non-trivial question which version, if any, of the weak gravity conjecture for domain walls should hold. In particular, we show that string compactifications with branes of different dimensions wrapped on different cycles lead to a `geometric weak gravity conjecture' relating volumes of cycles, norms of corresponding forms and the volume of the compact space. Imposing this `geometric conjecture', e.g.~on the basis of the more widely accepted weak gravity conjecture for particles, provides at least some support for the (electric and magnetic) conjecture for domain walls.

hep-th↗

arXiv2016

Non-Equilibrium Random Matrix Theory : Transition Probabilities

In this letter we present an analytic method for calculating the transition probability between two random Gaussian matrices with given eigenvalue spectra in the context of Dyson Brownian motion. We show that in the Coulomb gas language, in large $N$ limit, memory of the initial state is preserved in the form of a universal linear potential acting on the eigenvalues. We compute the likelihood of any given transition as a function of time, showing that as memory of the initial state is lost, transition probabilities converge to those of the static ensemble.

cond-mat.stat-mech↗

arXiv2016

Vacuum energy sequestering and conformal symmetry

In a series of recent papers Kaloper and Padilla proposed a mechanism to sequester standard model vacuum contributions to the cosmological constant. We study the consequences of embedding their proposal into a fully local quantum theory. In the original work, the bare cosmological constant $Λ$ and a scaling parameter $λ$ are introduced as global fields. We find that in the local case the resulting Lagrangian is that of a spontaneously broken conformal field theory where $λ$ plays the role of the dilaton. A vanishing or a small cosmological constant is thus a consequence of the underlying conformal field theory structure.

hep-th↗

arXiv2016

Pole Inflation - Shift Symmetry and Universal Corrections

An appealing explanation for the Planck data is provided by inflationary models with a singular non-canonical kinetic term: a Laurent expansion of the kinetic function translates into a potential with a nearly shift-symmetric plateau in canonical fields. The shift symmetry can be broken at large field values by including higher-order poles, which need to be hierarchically suppressed in order not to spoil the inflationary plateau. The herefrom resulting corrections to the inflationary dynamics and predictions are shown to be universal at lowest order and possibly to induce power loss at large angular scales. At lowest order there are no corrections from a pole of just one order higher and we argue that this phenomenon is related to the well-known extended no-scale structure arising in string theory scenarios. Finally, we outline which other corrections may arise from string loop effects.

hep-th↗

arXiv2016

Starobinsky-Type Inflation from $α'$-Corrections

Working in the Large Volume Scenario (LVS) of IIB Calabi-Yau flux compactifications, we construct inflationary models from recently computed higher derivative $(α')^3$-corrections. Inflation is driven by a Kaehler modulus whose potential arises from the aforementioned corrections, while we use the inclusion of string loop effects just to ensure the existence of a graceful exit when necessary. The effective inflaton potential takes a Starobinsky-type form $V=V_0(1-e^{-νϕ})^2$, where we obtain one set-up with $ν=-1/\sqrt{3}$ and one with $ν=2/\sqrt{3}$ corresponding to inflation occurring for increasing or decreasing $ϕ$ respectively. The inflationary observables are thus in perfect agreement with PLANCK, while the two scenarios remain observationally distinguishable via slightly varying predictions for the tensor-to-scalar ratio $r$. Both set-ups yield $r\simeq (2\ldots 7)\,\times 10^{-3}$. They hence realise inflation with moderately large fields $\left(Δϕ\sim 6\thinspace M_{Pl}\right)$ without saturating the Lyth bound. Control over higher corrections relies in part on tuning underlying microscopic parameters, and in part on intrinsic suppressions. The intrinsic part of control arises as a leftover from an approximate effective shift symmetry at parametrically large volume.

hep-th↗

arXiv2015

String Cosmology - Large-Field Inflation in String Theory

This is a short review of string cosmology. We wish to connect string-scale physics as closely as possible to observables accessible to current or near-future experiments. Our possible best hope to do so is a description of inflation in string theory. The energy scale of inflation can be as high as that of Grand Unification (GUT). If this is the case, this is the closest we can possibly get in energy scales to string-scale physics. Hence, GUT-scale inflation may be our best candidate phenomenon to preserve traces of string-scale dynamics. Our chance to look for such traces is the primordial gravitational wave, or tensor mode signal produced during inflation. For GUT-scale inflation this is strong enough to be potentially visible as a B-mode polarization of the cosmic microwave background (CMB). Moreover, a GUT-scale inflation model has a trans-Planckian excursion of the inflaton scalar field during the observable amount of inflation. Such large-field models of inflation have a clear need for symmetry protection against quantum corrections. This makes them ideal candidates for a description in a candidate fundamental theory like string theory. At the same time the need of large-field inflation models for UV completion makes them particularly susceptible to preserve imprints of their string-scale dynamics in the inflationary observables, the spectral index $n_s$ and the fractional tensor mode power $r$. Hence, we will focus this review on axion monodromy inflation as a mechanism of large-field inflation in string theory.

hep-th↗

arXiv2015

Bifid Throats for Axion Monodromy Inflation

We construct a simple explicit local geometry providing a `bifid throat' for 5-brane axion monodromy. A bifid throat is a throat that splits into two daughter throats in the IR, containing a homologous 2-cycle family reaching down into each daughter throat. Our example consists of a deformed $\mathbb{Z}_3\times\mathbb{Z}_2$ orbifold of the conifold, which provides us with an explicit holographic dual of the bifid throat including D3-branes and fractional 5-branes at the toric singularities of our setup. Having the holographic description in terms of the dual gauge theory allows us to address the effect of 5-brane-antibrane pair backreaction including the warping effects. This leads to the size of the backreaction being small and controllable after imposing proper normalization of the inflaton potential and hence the warping scales.

hep-th↗

arXiv2015

Higher-Derivative Supergravity and Moduli Stabilization

We review the ghost-free four-derivative terms for chiral superfields in $\mathcal{N}=1$ supersymmetry and supergravity. These terms induce cubic polynomial equations of motion for the chiral auxiliary fields and correct the scalar potential. We discuss the different solutions and argue that only one of them is consistent with the principles of effective field theory. Special attention is paid to the corrections along flat directions which can be stabilized or destabilized by the higher-derivative terms. We then compute these higher-derivative terms explicitly for the type IIB string compactified on a Calabi-Yau orientifold with fluxes via Kaluza-Klein reducing the $(α')^3 R^4$ corrections in ten dimensions for the respective $\mathcal{N}=1$ Kähler moduli sector. We prove that together with flux and the known $(α')^3$-corrections the higher-derivative term stabilizes all Calabi-Yau manifolds with positive Euler number, provided the sign of the new correction is negative.

hep-th↗

arXiv2015

Disentangling the $f(R)$ - Duality

Motivated by UV realisations of Starobinsky-like inflation models, we study generic exponential plateau-like potentials to understand whether an exact $f(R)$-formulation may still be obtained when the asymptotic shift-symmetry of the potential is broken for larger field values. Potentials which break the shift symmetry with rising exponentials at large field values only allow for corresponding $f(R)$-descriptions with a leading order term $R^{n}$ with $1<n<2$, regardless of whether the duality is exact or approximate. The $R^2$-term survives as part of a series expansion of the function $f(R)$ and thus cannot maintain a plateau for all field values. We further find a lean and instructive way to obtain a function $f(R)$ describing $m^2ϕ^2$-inflation which breaks the shift symmetry with a monomial, and corresponds to effectively logarithmic corrections to an $R+R^2$ model. These examples emphasise that higher order terms in $f(R)$-theory may not be neglected if they are present at all. Additionally, we relate the function $f(R)$ corresponding to chaotic inflation to a more general Jordan frame set-up. In addition, we consider $f(R)$-duals of two given UV examples, both from supergravity and string theory. Finally, we outline the CMB phenomenology of these models which show effects of power suppression at low-$\ell$.

hep-th↗

arXiv2015

Challenges for Large-Field Inflation and Moduli Stabilization

We analyze the interplay between Kähler moduli stabilization and chaotic inflation in supergravity. While heavy moduli decouple from inflation in the supersymmetric limit, supersymmetry breaking generically introduces non-decoupling effects. These lead to inflation driven by a soft mass term, $m_φ^2 \sim m m_{3/2}$, where $m$ is a supersymmetric mass parameter. This scenario needs no stabilizer field, but the stability of moduli during inflation imposes a large supersymmetry breaking scale, $m_{3/2} \gg H$, and a careful choice of initial conditions. This is illustrated in three prominent examples of moduli stabilization: KKLT stabilization, Kähler Uplifting, and the Large Volume Scenario. Remarkably, all models have a universal effective inflaton potential which is flattened compared to quadratic inflation. Hence, they share universal predictions for the CMB observables, in particular a lower bound on the tensor-to-scalar ratio, $r \gtrsim 0.05$.

hep-th↗

arXiv2015

Power Spectrum of Inflationary Attractors

Inflationary attractors predict the spectral index and tensor-to-scalar ratio to take specific values that are consistent with Planck. An example is the universal attractor for models with a generalised non-minimal coupling, leading to Starobinsky inflation. In this paper we demonstrate that it also predicts a specific relation between the amplitude of the power spectrum and the number of e-folds. The length and height of the inflationary plateau are related via the non-minimal coupling: in a wide variety of examples, the observed power normalisation leads to at least 55 flat e-foldings. Prior to this phase, the inflationary predictions vary and can account for the observational indications of power loss at large angular scales.

hep-th↗

arXiv2014

Drifting Oscillations in Axion Monodromy

We study the pattern of oscillations in the primordial power spectrum in axion monodromy inflation, accounting for drifts in the oscillation period that can be important for comparing to cosmological data. In these models the potential energy has a monomial form over a super-Planckian field range, with superimposed modulations whose size is model-dependent. The amplitude and frequency of the modulations are set by the expectation values of moduli fields. We show that during the course of inflation, the diminishing energy density can induce slow adjustments of the moduli, changing the modulations. We provide templates capturing the effects of drifting moduli, as well as drifts arising in effective field theory models based on softly broken discrete shift symmetries, and we estimate the precision required to detect a drifting period. A non-drifting template suffices over a wide range of parameters, but for the highest frequencies of interest, or for sufficiently strong drift, it is necessary to include parameters characterizing the change in frequency over the e-folds visible in the CMB. We use these templates to perform a preliminary search for drifting oscillations in a part of the parameter space in the Planck nominal mission data.

hep-th↗

arXiv2014

Towards Natural Inflation in String Theory

We provide type IIB string embeddings of two axion variants of natural inflation. We use a combination of RR 2 form axions as the inflaton field and have its potential generated by non perturbative effects in the superpotential. Besides giving rise to inflation, the models developed take into account the stabilization of the compact space, both in the KKLT and large volume scenario regimes, an essential condition for any semi-realistic model of string inflation.

hep-th↗

arXiv2014

Hierarchical Axion Inflation

We propose a new field theory mechanism for generating an effective trans-Planckian decay constant from sub-Planckian ones. Using the minimal two axions and a hierarchy between two axion decay constants is sufficient for realizing inflation through non-perturbative effects only and with minimal tuning. The inflationary motion is kept entirely within a sub-Planckian domain. We outline possible strategies of embedding the model in a string theory setup.

hep-th↗

arXiv2014

The Powers of Monodromy

Flux couplings to string theory axions yield super-Planckian field ranges along which the axion potential energy grows. At the same time, other aspects of the physics remain essentially unchanged along these large displacements, respecting a discrete shift symmetry with a sub-Planckian period. After a general overview of this monodromy effect and its application to large-field inflation, we present new classes of specific models of monodromy inflation, with monomial potentials $μ^{4-p}ϕ^p$. A key simplification in these models is that the inflaton potential energy plays a leading role in moduli stabilization during inflation. The resulting inflaton-dependent shifts in the moduli fields lead to an effective flattening of the inflaton potential, i.e. a reduction of the exponent from a fiducial value $p_0$ to $p<p_0$. We focus on examples arising in compactifications of type IIB string theory on products of tori or Riemann surfaces, where the inflaton descends from the NS-NS two-form potential $B_2$, with monodromy induced by a coupling to the R-R field strength $F_1$. In this setting we exhibit models with $p=2/3,4/3,2,$ and $3$, corresponding to predictions for the tensor-to-scalar ratio of $r\approx 0.04, 0.09, 0.13,$ and $0.2$, respectively. Using mirror symmetry, we also motivate a second class of examples with the role of the axions played by the real parts of complex structure moduli, with fluxes inducing monodromy.

hep-th↗