General analysis of dark radiation in sequestered string models

Published for SISSA by Springer Received: November 30, 2015 Accepted: December 14, 2015 Published: December 22, 2015 General analysis of dark radiation in sequestered string models a ICTP, Strada Costiera 11, Trieste 34014, Italy b Dipartimento di Fisica e Astronomia, Università di Bologna, via Irnerio 46, 40126 Bologna, Italy c INFN, Sezione di Bologna, via Irnerio 46, 40126 Bologna, Italy E-mail: , Abstract: We perform a general analysis of axionic dark radiation produced from the decay of the lightest modulus in the sequestered LARGE Volume Scenario. We discuss several cases depending on the form of the Kähler metric for visible sector matter fields and the mechanism responsible for achieving a de Sitter vacuum. The leading decay channels which determine dark radiation predictions are to hidden sector axions, visible sector Higgses and SUSY scalars depending on their mass. We show that in most of the parameter space of split SUSY-like models squarks and sleptons are heavier than the lightest modulus. Hence dark radiation predictions previously obtained for MSSM-like cases hold more generally also for split SUSY-like cases since the decay channel to SUSY scalars is kinematically forbidden. However the inclusion of string loop corrections to the Kähler potential gives rise to a parameter space region where the decay channel to SUSY scalars opens up, leading to a significant reduction of dark radiation production. In this case, the simplest model with a shift-symmetric Higgs sector can suppress the excess of dark radiation ∆Neff to values as small as 0.14, in perfect agreement with current experimental bounds. Depending on the exact mass of the SUSY scalars all values in the range 0.14 . ∆Neff . 1.6 are allowed. Interestingly dark radiation overproduction can be avoided also in the absence of a Giudice-Masiero coupling. Keywords: Cosmology of Theories beyond the SM, Supergravity Models, Superstring Vacua, Supersymmetry Breaking ArXiv ePrint: 1511.05447 Open Access, c The Authors. Article funded by SCOAP3 . doi:10.1007/JHEP12(2015)152 JHEP12(2015)152 Michele Cicolia,b,c and Francesco Muiab,c Contents 1 2 Sequestered LARGE Volume Scenario 2.1 Effective field theory setup 2.2 De Sitter moduli stabilisation 2.3 F- and D-terms 2.4 Soft SUSY breaking terms 2.4.1 Gaugino masses 2.4.2 Scalar masses 2.4.3 µ and Bµ terms 5 6 7 8 8 8 8 10 3 Dark radiation in sequestered models 3.1 Dark radiation from moduli decays 3.2 Light relativistic axions in LVS models 3.3 Volume modulus decay channels 3.3.1 Decays into hidden sector fields 3.3.2 Decays into visible sector fields 3.4 Dark radiation predictions 3.4.1 MSSM-like case 3.4.2 Split SUSY-like case 10 11 12 12 12 13 16 16 16 4 Conclusions 26 1 Introduction According to the cosmological Standard Model (SM), neutrinos were in thermal equilibrium at early times and decoupled at temperatures of order 1 MeV. This decoupling left behind a cosmic neutrino background which has been emitted much earlier than the analogous cosmic microwave background (CMB). Due to the weakness of the weak interactions, this cosmic neutrino background cannot be detected directly, and so goes under the name of ‘dark radiation’. Its contribution to the total energy density ρtot is parameterised in terms of the effective number of neutrino-like species Neff as: !   7 4 4/3 ρtot = ργ 1 + (1.1) Neff . 8 11 The SM predictions for Neff are Neff = 3 during Big Bang Nucleosynthesis (BBN) and Neff = 3.046 at CMB times since neutrinos get slightly reheated when electrons and positrons annihilate. Any departure from these values would be a clear signal of physics –1– JHEP12(2015)152 1 Introduction –2– JHEP12(2015)152 beyond the SM due to the presence of extra dark radiation controlled by the parameter ∆Neff ≡ Neff − Neff,SM . Given that Neff is positively correlated with the present value of the Hubble constant H0 , the comparison between indirect estimates of H0 from CMB experiments and direct astrophysical measurements of H0 could signal the need for extra dark radiation. The Planck 2013 value of the Hubble constant is H0 = (67.3 ± 1.2) km s−1 Mpc−1 (68% CL) [1] which is in tension at 2.5σ with the Hubble Space Telescope (HST) value H0 = (73.8 ± 2.4) km s−1 Mpc−1 (68% CL) [2]. Hence the Planck 2013 estimate of Neff with this HST ‘H0 prior’ is Neff = 3.62+0.50 −0.48 (95% CL) [1] which is more than 2σ away from the SM value and gives ∆Neff ≤ 1.07 at 2σ. However the HST Cepheid data have been reanalysed by [3] who found the different value H0 = (70.6 ± 3.3) km s−1 Mpc−1 (68% CL) which is within 1σ of the Planck 2015 estimate H0 = (67.3 ± 1.0) km s−1 Mpc−1 (68% CL) [4]. Hence the Planck 2015 collaboration performed a new estimate of Neff without using any ‘H0 prior’ and obtaining Neff = 3.13 ± 0.32 (68% CL) [4] which is perfectly consistent with the SM value and gives ∆Neff ≤ 0.72 at around 2σ. This result might seem to imply that extra dark radiation is ruled out but this naive interpretation can be misleading since larger Neff corresponds to larger H0 and there is still an unresolved controversy in the direct measurement of H0 . In fact the Planck 2015 paper [4] analyses also the case with the prior ∆Neff = 0.39 obtaining the result H0 = (70.6 ± 1.0) km s−1 Mpc−1 (68% CL) which is even in better agreement with the new HST estimate of H0 performed in [3]. Thus we stress that trustable direct astrophysical measurements of H0 are crucial in order to obtain reliable bounds on Neff . Neff is also constrained by measurements of primordial light element abundances. The Planck 2015 estimate of Neff based on the helium primordial abundance and combined with the measurements of [5] is Neff = 3.11+0.59 −0.57 (95% CL) giving ∆Neff ≤ 0.65 at 2σ [4]. However measurements of light element abundances are difficult and often affected by systematic errors, and so also in this case there is still some controversy in the literature since [6] reported a larger helium abundance that, in turn, leads to Neff = 3.58 ± 0.50 (99% CL) which is 3σ away from the SM value and gives ∆Neff ≤ 1.03 at 3σ. Due to all these experimental considerations, in the rest of this paper we shall consider ∆Neff . 1 as a reference upper bound for the presence of extra dark radiation. Extra neutrino-like species can be produced in any beyond the SM theory which features hidden sectors with new relativistic degrees of freedom (dof ). In particular, extra dark radiation is naturally generated when reheating is driven by the decay of a gauge singlet since in this case there is no a priori good reason to suppress the branching ratio into hidden sector light particles [7–9]. This situation is reproduced in string models of the early universe due to the presence of gravitationally coupled moduli which get displaced from their minimum during inflation, start oscillating when the Hubble scale reaches their mass, quickly come to dominate the energy density of the universe since they redshift as (...truncated)