PHYSICAL REVIEW LETTERS 122, 091802 (2019) Can the Inflaton Also Be a Weakly Interacting Massive Particle? Dan Hooper,1,2,3 Gordan Krnjaic,1 Andrew J. Long,2 and Samuel D. McDermott1 1Fermi National Accelerator Laboratory, Theoretical Astrophysics Group, Batavia, Illinois 60510, USA 2University of Chicago, Kavli Institute for Cosmological Physics, Chicago, Illinois 60637, USA 3University of Chicago, Department of Astronomy and Astrophysics, Chicago, Illinois 60637, USA (Received 17 July 2018; revised manuscript received 4 February 2019; published 6 March 2019) We propose a class of models in which a stable inflaton is produced as a thermal relic in the early Universe and constitutes the dark matter. We show that inflaton annihilations can efficiently reheat the Universe, and identify several examples of inflationary potentials that can accommodate all cosmic microwave background observables and in which the inflaton dark matter candidate has a weak scale mass. As a simple example, we consider annihilations that take place through a Higgs portal interaction, leading to encouraging prospects for future direct detection experiments. DOI: 10.1103/PhysRevLett.122.091802 Introduction.—Two of the most pressing problems in matter. We present a wide range of inflationary scenarios in cosmology concern the unknown physics of dark matter which the inflaton can play the role of a thermal relic that and inflation. Although the existence of dark matter is also serves as a viable dark matter candidate. strongly supported by a variety of observations, the particle In order for the inflaton to be a thermal dark matter identity of this substance remains entirely unknown. candidate, it must be stable and it must freeze out of Similarly, whereas cosmological inflation is motivated equilibrium in the early Universe to yield an acceptable by the flatness and horizon problems [1], and it is supported relic abundance. This requires the dark matter to possess by the adiabatic and approximately scale-invariant pertur- interactions that allow it to annihilate with a cross section bations observed in the cosmic microwave background of approximately σv ≈ 2 × 10−26 cm3=s and to have a (CMB) [2–6], we know little about this period of our mass between approximately 10 MeV and 100 TeV. cosmic history. In this Letter, we consider the possibility Annihilations through these same interactions must take that these two seemingly unrelated phenomena are in fact place at the end of inflation and be efficient enough to intimately connected. More specifically, we explore a broad reheat the Universe to a high temperature. This produces a class of models in which the field responsible for inflation thermal bath of both standard model particles and inflatons. (i.e., the inflaton) is also a stable particle whose population The weak scale inflatons then proceed to freeze out of freezes out of thermal equilibrium in the early Universe to equilibrium in the standard way, resulting in the measured constitute the dark matter. We refer to this scenario as abundance of cold, collisionless dark matter. WIMPflation. Inflationary dynamics.—We consider a class of scenarios The possibility that a single particle could play the dual in which the inflaton ϕ is a real scalar singlet whose roles of inflaton and dark matter was mentioned in interactions respect a Z2 symmetry, ensuring its stability in Refs. [7,8], and studied with more detail in Refs. [9–30]. the vacuum. The dynamics of ϕ are described by the In particular, McDonald and collaborators [14,17,23] following Lagrangian: considered a specific and phenomenologically viable model in which the dark matter candidate is also the 1 μν L ¼ g ∂μϕ∂νϕ − VðϕÞþL ; ð1Þ inflaton, possessing a nonminimal coupling to gravity. In 2 int this Letter, our goal is to develop a more general outlook on ϕ L WIMPflation by identifying the features that are generi- where Vð Þ is the inflaton potential and int describes the cally required of a model that can simultaneously satisfy all interactions that enable inflaton annihilation to both reheat existing constraints pertaining to both inflation and dark the Universe and later to result in an acceptable thermal relic abundance. For the inflaton to be a viable thermal relic, its mass must lie in the range 10 MeV ≲ mϕ ≲ 100 TeV [31,32]. Thus Published by the American Physical Society under the terms of we adopt an inflaton potential that includes one term to the Creative Commons Attribution 4.0 International license. generate the inflaton mass plus a second term to drive Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, inflation (without contributing to mϕ). Potentials that and DOI. Funded by SCOAP3. satisfy these criteria can be written as 0031-9007=19=122(9)=091802(6) 091802-1 Published by the American Physical Society PHYSICAL REVIEW LETTERS 122, 091802 (2019) arises from the ϕ4 case in the presence of a nonminimal coupling to gravity of the form ϕ2R [14,17,44] and is similar to pure natural inflation [45]. As a paradigmatic example for the interaction term in Eq. (1), we will consider a Higgs portal operator [46,47], κ L − H†Hϕ2 int ¼ 2 ; ð4Þ where κ is a dimensionless mixed quartic coupling and H is the standard model Higgs doublet. In the presence of a background inflaton field, ϕ ≠ 0, the Higgs boson acquires 2 −μ2 κϕ2 2 an effective squared mass given by mh ¼ H þ = 2 where μH ∼ 10 GeV sets the mass of the standard model Higgs boson at low temperatures. For the models we FIG. 1. The inflaton potentials considered in this study are consider, mh is always much larger than the rate of shown here normalized to the value that they take 60 e foldings Hubble expansion during inflation. For this reason, quan- before the end of inflation. The colored dots denote the point at tum fluctuations of the Higgs field are negligible, and the which inflation ends in each model. dynamics of inflation are entirely dominated by the second term in Eq. (2). We emphasize that H ¼ 0 is a solution to 1 the classical equations of motion throughout the entire ϕ 2 ϕ2 λϕ4 ϕ ϕ Vð Þ¼2 mϕ þ 0fð = 0Þ; ð2Þ process of inflation: the Higgs can only be “unfrozen” when the phi field value crosses the origin during reheating. where ϕ0 is a dimensionful constant, the function fðϕ=ϕ0Þ Thus, our potential reduces to the case of single-field slow has a vanishing second derivative at the origin, and thus, mϕ roll for the purposes of inflationary dynamics. Even if H is the inflaton’s mass in the vacuum. We consider the were initially displaced from the minimum of its potential, following functional forms for the term in the potential that such that there is an early phase of multifield inflation, we drives inflationary dynamics: observe that the H field has a steeper potential than the ϕ H 8 field does, and it is reasonable to expect will reach the 4 ϕ > x origin while is still slowly rolling. The standard period of > ϕ > 4 single-field slow-roll inflation, driven exclusively by , > arctan x <> would in this way come to dominate the Universe before tanh4 x ϕ ϕ reheating. fðx ¼ = 0Þ¼> 2 2 : ð3Þ > ½1 − expð−x Þ We emphasize that the second term in Eq. (2) is > responsible for the phenomenology of inflation whereas > ð1 − cos xÞ2 > Eq. (4) and the first term in Eq. (2) set the inflaton : 4 2 2 x =ð1 þ x Þ annihilation cross section and mass. The dark matter and inflationary dynamics are therefore largely modular and 4 The first of these is the ϕ potential, which is the simplest independent of one another within this class of models. example that meets the requirements listed above. As is If the field ϕ is displaced from the minimum of its well known, however, ϕ4 inflation predicts a large tensor- potential it can drive cosmological inflation and induce the to-scalar ratio, and is ruled out by modern CMB observa- perturbations that we eventually observe in the CMB. For tions [5,6]. We include it here for completeness and for an each of the functions listed in Eq. (3), we calculate the illuminating contrast with the other potentials under slow-roll parameters, which are defined as follows [48]: consideration. Several of the examples described in Eq. (3) are similar 1 V0 2 V00 ϵ ≡ m2 ; η ≡ m2 ; ð5Þ to those found in well-known models [33]. The function 2 Pl V Pl V arctanðϕ=ϕ0Þ was originally used in Ref. [34] as a toy example of a potential that leads to a rapidly varying where m ≃ 2.4 × 1018 GeV is the reduced Planck mass. 4 Pl equation of state parameter. The potentials tanh ðϕ=ϕ0Þ Slow-roll inflation occurs when the inflaton field is nearly 2 2 and f1 − exp½−ðϕ=ϕ0Þ g are variations of the T-model homogeneous in a Hubble patch and ϵ; η ≪ 1. We define α ϵ 1 and E-model realizations of the -attractor scenario the end of inflation, tend, as the time when ¼ .CMB – 1 − ϕ ϕ 2 ϕ [35 38]. The potential ½ cosð = 0Þ is similar to those observables probe the inflaton potential at CMB, which is ≈ 50–60 found in natural inflation [39,40] but dominated by a higher the value of the inflaton field NCMB e foldings 4 2 2 harmonic [41–43]. Finally, the potential ϕ =½1 þðϕ=ϕ0Þ before the end of inflation: 091802-2 PHYSICAL REVIEW LETTERS 122, 091802 (2019) Vðϕ Þ λ 10−2 A CMB ∼ 2 10−9 : s ¼ 24π2 4 ϵ × 5 10−9 ϵ ð7Þ mPl × Thus λ must be very small in order to accommodate obs −9 Planck’s measurement of As ¼ 2.196 × 10 [6].