arXiv subjects

Alexander Westphal

Publications and source records attributed to Alexander Westphal.

At least 73 records · Page 4Linked to original sources

arXiv2014

Just enough inflation: power spectrum modifications at large scales

We show that models of `just enough' inflation, where the slow-roll evolution lasted only $50-60$ e-foldings, feature modifications of the CMB power spectrum at large angular scales. We perform a systematic and model-independent analysis of any possible non-slow-roll background evolution prior to the final stage of slow-roll inflation. We find a high degree of universality since most common backgrounds like fast-roll evolution, matter or radiation-dominance give rise to a power loss at large angular scales and a peak together with an oscillatory behaviour at scales around the value of the Hubble parameter at the beginning of slow-roll inflation. Depending on the value of the equation of state parameter, different pre-inflationary epochs lead instead to an enhancement of power at low-$\ell$, and so seem disfavoured by recent observational hints for a lack of CMB power at $\ell\lesssim 40$. We also comment on the importance of initial conditions and the possibility to have multiple pre-inflationary stages.

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arXiv2014

Chaotic Inflation in Supergravity after Planck and BICEP2

We discuss the general structure and observational consequences of some of the simplest versions of chaotic inflation in supergravity in relation to the data by Planck 2013 and BICEP2. We show that minimal modifications to the simplest quadratic potential are sufficient to provide a controllable tensor mode signal and a suppression of CMB power at large angular scales.

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arXiv2014

$R^2\log R$ quantum corrections and the inflationary observables

We study a model of inflation with terms quadratic and logarithmic in the Ricci scalar, where the gravitational action is $f(R)=R+αR^2+βR^2 \ln R$. These terms are expected to arise from one loop corrections involving matter fields in curved space-time. The spectral index $n_s$ and the tensor to scalar ratio yield $10^{-4}\lesssim r\lesssim0.03$ and $0.94\lesssim n_s \lesssim 0.99$. i.e. $r$ is an order of magnitude bigger or smaller than the original Starobinsky model which predicted $r\sim 10^{-3}$. Further enhancement of $r$ gives a scale invariant $n_s\sim 1$ or higher. Other inflationary observables are $d n_s/d\ln k \gtrsim -5.2 \times 10^{-4},\, μ\lesssim 2.1 \times 10^{-8} ,\, y \lesssim 2.6 \times 10^{-9}$. Despite the enhancement in $r$, if the recent BICEP2 measurement stands, this model is disfavoured.

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arXiv2014

Relations between canonical and non-canonical inflation

We look for potential observational degeneracies between canonical and non-canonical models of inflation of a single field $ϕ$. Non-canonical inflationary models are characterized by higher than linear powers of the standard kinetic term $X$ in the effective Lagrangian $p(X,ϕ)$ and arise for instance in the context of the Dirac-Born-Infeld (DBI) action in string theory. An on-shell transformation is introduced that transforms non-canonical inflationary theories to theories with a canonical kinetic term. The 2-point function observables of the original non-canonical theory and its canonical transform are found to match in the case of DBI inflation.

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arXiv2014

Evading the Lyth Bound in Hybrid Natural Inflation

Generically, the gravitational-wave or tensor-mode contribution to the primordial curvature spectrum of inflation is tiny if the field-range of the inflaton is much smaller than the Planck scale. We show that this pessimistic conclusion is naturally avoided in a rather broad class of small-field models. More specifically, we consider models where an axion-like shift symmetry keeps the inflaton potential flat (up to non-perturbative cosine-shaped modulations), but inflation nevertheless ends in a waterfall-regime, as is typical for hybrid inflation. In such hybrid natural inflation scenarios (examples are provided by Wilson line inflation and fluxbrane inflation), the slow-roll parameter $ε$ can be sizable during an early period (relevant for the CMB spectrum). Subsequently, $ε$ quickly becomes very small before the tachyonic instability eventually terminates the slow roll regime. In this scenario, one naturally generates a considerable tensor-mode contribution in the curvature spectrum, collecting nevertheless the required amount of e-foldings during the final period of inflation. While non-observation of tensors by Planck is certainly not a problem, a discovery in the medium to long term future is realistic.

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arXiv2013

On Moduli Spaces in $\bf{AdS_4}$ Supergravity

We study the structure of the supersymmetric moduli spaces of ${\cal N}=1$ and ${\cal N}=2$ supergravity theories in $AdS_4$ backgrounds. In the ${\cal N}=1$ case, the moduli space cannot be a complex submanifold of the Kähler field space, but is instead real with respect to the inherited complex structure. In ${\cal N}=2$ supergravity the same result holds for the vector multiplet moduli space, while the hypermultiplet moduli space is a Kähler submanifold of the quaternionic-Kähler field space. These findings are in agreement with AdS/CFT considerations.

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arXiv2013

Heterotic Moduli Stabilisation

We perform a systematic analysis of moduli stabilisation for weakly coupled heterotic string theory compactified on manifolds which are Calabi-Yau up to alpha' effects. We review how to fix all geometric and bundle moduli in a supersymmetric way by fractional fluxes, the requirement of a holomorphic gauge bundle, D-terms, higher order perturbative contributions to W, non-perturbative and threshold effects. We then show that alpha' corrections to K lead to new stable Minkowski (or dS) vacua where the complex structure moduli Z and the dilaton are fixed supersymmetrically, while the fixing of the Kahler moduli at a lower scale leads to spontaneous SUSY breaking. The minimum lies at moderately large volumes of all geometric moduli, at a perturbative string coupling and at the right value of the GUT coupling. We also give a dynamical derivation of anisotropic compactifications which allow for gauge coupling unification around 10^16 GeV. The gravitino mass can be anywhere between the GUT and TeV scale depending on the fixing of the Z-moduli. In general, these are fixed by turning on background fluxes, leading to a gravitino mass around the GUT scale since the heterotic 3-form flux does not contain enough freedom to tune W to small values. Moreover accommodating the observed value of the cosmological constant (CC) is a challenge. Low-energy SUSY could instead be obtained in particular situations where the gauge bundle is holomorphic only at a point-like sub-locus of Z-moduli space, or where the number of Z-moduli is small (like orbifold models), since in these cases one may fix all moduli without turning on any quantised flux. However tuning the CC is even more of a challenge in these cases. Another option is to focus on non-complex manifolds since these allow for new geometric fluxes which can be used to tune W and the CC, even if their moduli space is presently only poorly understood.

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arXiv2013

Low-l CMB Power Loss in String Inflation

The lack of power on large scales (l < 40) might have been observed by the PLANCK satellite. We argue that this putative feature can be explained by a phase of fast roll at the onset of inflation. We show that in the context of single field models what is required is an asymmetric inflection point model of which fibre inflation is a string motivated example. We study the ability of fibre inflation to generate a suppression of the CMB 2-point function power at low l, finding that the potential derived from string loops is not steep enough for this purpose. We introduce a steeper contribution to the potential, that dominates away from the inflationary region, and show that if properly tuned it can indeed lead to a spectrum with lack of power at large scales.

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arXiv2013

Accidental Inflation from Kähler Uplifting

We analyze the possibility of realizing inflation with a subsequent dS vacuum in the Kähler uplifting scenario. The inclusion of several quantum corrections to the 4d effective action evades previous no-go theorems and allows for construction of simple and successful models of string inflation. The predictions of several benchmark models are in accord with current observations, i.e., a red spectral index, negligible non-gaussianity, and spectral distortions similar to the simplest models of inflation. A particularly interesting subclass of models are "left-rolling" ones, where the overall volume of the compactified dimensions shrinks during inflation. We call this phenomenon "inflation by deflation" (IBD), where deflation refers to the internal manifold. This subclass has the appealing features of being insensitive to initial conditions, avoiding the overshooting problem, and allowing for observable running $α$ ~ 0.012 and enhanced tensor-to-scalar ratio $r$ ~ $10^{-5}$. The latter results differ significantly from many string inflation models.

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arXiv2013

Resonant non-Gaussianity with equilateral properties

We discuss the effect of superimposing multiple sources of resonant non-Gaussianity, which arise for instance in models of axion inflation. The resulting sum of oscillating shape contributions can be used to "Fourier synthesize" different non-oscillating shapes in the bispectrum. As an example we reproduce an approximately equilateral shape from the superposition of ${\cal O}(10)$ oscillatory contributions with resonant shape. This implies a possible degeneracy between the equilateral-type non-Gaussianity typical of models with non-canonical kinetic terms, such as DBI inflation, and an equilateral-type shape arising from a superposition of resonant-type contributions in theories with canonical kinetic terms. The absence of oscillations in the 2-point function together with the structure of the resonant $N$-point functions, imply that detection of equilateral non-Gaussianity at a level greater than the PLANCK sensitivity of $f_{NL}\sim{\cal O}(5)$ will rule out a resonant origin. We comment on the questions arising from possible embeddings of this idea in a string theory setting.

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arXiv2013

The Scale of Inflation in the Landscape

We determine the frequency of regions of small-field inflation in the Wigner landscape as an approximation to random supergravities/type IIB flux compactifications. We show that small-field inflation occurs exponentially more often than large-field inflation The power of primordial gravitational waves from inflation is generically tied to the scale of inflation. For small-field models this is below observational reach. However, we find small-field inflation to be dominated by the highest inflationary energy scales compatible with a sub-Planckian field range. Hence, we expect a typical tensor-to-scalar ratio $r\sim {\cal O}(10^{-3})$ currently undetectable in upcoming CMB measurements.

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arXiv2013

Metastable Electroweak Vacuum: Implications for Inflation

Within the Standard Model, the current Higgs and top quark data favor metastability of the electroweak vacuum, although the uncertainties are still significant. The true vacuum is many orders of magnitude deeper than ours and the barrier separating the two is tiny compared to the depth of the well. This raises a cosmological question: how did the Higgs field get trapped in the shallow minimum and why did it stay there during inflation? The Higgs initial conditions before inflation must be fine--tuned to about one part in 10^8 in order for the Higgs field to end up in the right vacuum. In this note, we show that these problems can be resolved if there is a small positive coupling between the Higgs and the inflaton.

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arXiv2013

Validity of the kink approximation to the tunneling action

Coleman tunneling in a general scalar potential with two non-degenerate minima is known to have an approximation in terms of a piecewise linear triangular-shaped potential with sharp 'kinks' at the place of the local minima. This approximate potential has a regime where the existence of the bounce solution needs the scalar field to 'wait' for some amount of Euclidean time at one of the 'kinks'. We discuss under which conditions a kink approximation of locally smooth 'cap' regions provides a good estimate for the bounce action.

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arXiv2012

Tensor modes on the string theory landscape

We attempt an estimate for the distribution of the tensor mode fraction $r$ over the landscape of vacua in string theory. The dynamics of eternal inflation and quantum tunneling lead to a kind of democracy on the landscape, providing no bias towards large-field or small-field inflation regardless of the class of measure. The tensor mode fraction then follows the number frequency distributions of inflationary mechanisms of string theory over the landscape. We show that an estimate of the relative number frequencies for small-field vs large-field inflation, while unattainable on the whole landscape, may be within reach as a regional answer for warped Calabi-Yau flux compactifications of type IIB string theory.

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arXiv2012

Finding all flux vacua in an explicit example

We explicitly construct all supersymmetric flux vacua of a particular Calabi-Yau compactification of type IIB string theory for a small number of flux carrying cycles and a given D3-brane tadpole. The analysis is performed in the large complex structure region by using the polynomial homotopy continuation method, which allows to find all stationary points of the polynomial equations that characterize the supersymmetric vacuum solutions. The number of vacua as a function of the D3 tadpole is in agreement with statistical studies in the literature. We calculate the available tuning of the cosmological constant from fluxes and extrapolate to scenarios with a larger number of flux carrying cycles. We also verify the range of scales for the moduli and gravitino masses recently found for a single explicit flux choice giving a Kähler uplifted de Sitter vacuum in the same construction.

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arXiv2012

Building an explicit de Sitter

We construct an explicit example of a de Sitter vacuum in type IIB string theory that realizes the proposal of Kähler uplifting. As the large volume limit in this method depends on the rank of the largest condensing gauge group we carry out a scan of gauge group ranks over the Kreuzer-Skarke set of toric Calabi-Yau threefolds. We find large numbers of models with the largest gauge group factor easily exceeding a rank of one hundred. We construct a global model with Kähler uplifting on a two-parameter model on $\mathbb{CP}^4_{11169}$, by an explicit analysis from both the type IIB and F-theory point of view. The explicitness of the construction lies in the realization of a D7 brane configuration, gauge flux and RR and NS flux choices, such that all known consistency conditions are met and the geometric moduli are stabilized in a metastable de Sitter vacuum with spontaneous GUT scale supersymmetry breaking driven by an F-term of the Kähler moduli.

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arXiv2012

A Toy Model For Single Field Open Inflation

Inflation in an open universe produced by Coleman-De Luccia (CDL) tunneling induces a friction term that is strong enough to allow for successful small-field inflation in models that would otherwise suffer from a severe overshoot problem. In this paper, we present a polynomial scalar potential which allows for a full analysis. This provides a simple model of single-field open inflation on a small-field inflection point after tunneling. We present numerical results and compare them with analytic approximations.

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arXiv2012