Dark radiation in anisotropic LARGE volume compactifications

Open Access 0 1 c The Authors. 0 1 0 1 Keble Road , Oxford, OX1 3NP , United Kingdom 1 Rudolph Peierls Centre for Theoretical Physics, University of Oxford Dark radiation is a compelling extension to CDM: current experimental results hint at Neff & 0.5, which is increased to Neff ' 1 if the recent BICEP2 results are included. In recent years dark radiation has been considered in the context of string theory models such as the LARGE Volume Scenario of type IIB string theory, forging a link between present-day cosmological observations and models of physics at the Planck scale. In this paper I consider an extension of the LARGE Volume Scenario in which the bulk volume is stabilised by two moduli instead of one. Consequently, the lightest modulus no longer corresponds to the compactification volume but instead to a transverse direction in the bulk geometry. I focus on scenarios in which sequestering of soft masses is achieved by localising the Standard Model on D3 branes at a singularity. The fraction of dark radiation produced in such models vastly exceeds experimental bounds, ruling out the sequestered LARGE Volume Scenario with two bulk moduli as a model of the early Universe. 1 Introduction 3.1 3.2 3.3 Fibred compactifications Leading decay modes Discussion and conclusions Prediction for the excess effective number of neutrino species In recent years there has been speculation about the possible existence of an additional relativistic matter component in the energy density of the Universe. This so-called dark radiation is motivated both theoretically and phenomenologically. In UV-complete quantum gravity frameworks such as string theory, the existence of light axion-like particles (ALPs) is commonplace string compactifications typically produce hundreds of moduli, with associated axions1 that are massless at the perturbative level due to shift symmetries. mological model implores us to ask: if dark matter, then why not dark radiation? The number of relativistic particle species is not protected by any symmetry, therefore there is no reason to assume a priori that the present-day radiation content of the Universe must consist of only photons and neutrinos. Dark radiation is conventionally described in terms of an excess effective number of Planck [1], high-l data from SPT [2] and ACT [3], WMAP 9-year polarisation data [4], BAO measurements, and the value of H0 observed by the Hubble Space Telescope [5], if one incorporates the recent discovery of primordial B-modes by BICEP2 [7]: using a 1Hereafter we make liberal use of the term axion to refer to axion-like particles in string compactifiCDM+r model with r = 0.2+00..0075, the authors of [8] find a preference for dark radiation, these results provide compelling hints for the possible existence of extra relativistic species. One of the key motivations for studying dark radiation is that it provides a means of testing models of physics at the Planck scale, such as string theory models. During inflation, the moduli of string compactifications are displaced from their final VEVs, such that when inflation ends they begin to oscillate about their global minimum. Since the moduli behave as non-relativistic matter, they eventually come to dominate the energy density of the Universe. The subsequent reheating of the visible Universe and production of hidden particle species is thus determined by the decay modes of moduli. In general, moduli have Planck-suppressed decay rates that scale as their mass cubed, have redshifted away by the time the lightest modulus decays. Hence reheating is driven solely by the decays of the lightest modulus to the visible sector. Furthermore, this implies that the lightest modulus is also dominantly responsible for dark radiation production. One phenomenologically appealing string theory model is the LARGE Volume Scenario (LVS) of type IIB string theory [1113]. In the most basic realisation of this scenario, the overall compactification volume V is determined by a single bulk cycle, while additional smaller blow-up cycles can support the visible sector, non-perturbative effects, and additional hidden sectors. The bulk volume is controlled by a Kahler modulus known as the volume modulus, which is stabilised at an exponentially large size due to a combination of lighter than all the other moduli, with a mass m are stabilised around the gravitino mass scale, m3/2 MP/V). V MP/V3/2 (whereas all the other moduli The branching fraction to dark radiation has been studied for this minimal LVS [14, 15] (see also [34]), in which the primordial abundance of dark radiation is determined by the decays of the volume modulus to visible- and hidden-sector particles. It turns out that with O(1) dimensionless coupling Z [16].2 The branching fraction to dark radiation can thus be computed: for the case of a shift symmetry in the Higgs sector, which implies of the moduli-induced axion problem [19], which is the statement that string models generically produce too much dark radiation via decays to axion-like particles. However, this tension is relaxed significantly if the BICEP2 results are included in the analysis: a 2This is a dimension-5 operator, so the overall coupling is Z/MP times a numerical factor. It is worthwhile to investigate whether or not extended models can yield a value of which the bulk volume is controlled by two Kahler moduli instead of one [2024]. One linear combination of these two moduli is the volume modulus, while a transverse flat direction remains unstabilised in the tree-level potential. Such a setup has a fibration structure and may lead to anisotropic modulus stabilisation. However, as I will discuss in section 2, anisotropy is not an essential requirement, and the conclusions of this paper apply to all fibred models with a particular sequestered structure. In fact, the crucial feature of these compactifications most relevant to our purposes is that the volume modulus is no longer the lightest modulus: the post-inflationary decays to visible and hidden radiation are instead controlled by the modulus parametrising the transverse direction. Hence this extension has non-trivial consequences for post-inflationary physics, and one might imagine that the above constraints on dark radiation could thus be avoided. The purpose of this paper is to analyse such a scenario and determine how the branching fraction to dark radiation is modified. The structure of this paper is as follows. In section 2 I describe and justify a twomodulus compactification scheme, for which I compute the decay modes, and deduce the Fibred compactifications Here we give an overview of some key features of fibred LVS models. First of all, the compactification volume V takes the form3 (1 corresponds to the fibre volume while the combination t1 2/1 gives the volume Such a model will also have h1,1 axions ai, so we can define complexified Kahler moduli, it turns out that we are focussing on energy scales at whi (...truncated)