EFTA02710829.pdf

Killing the Straw Man: Does BICEP Prove Inflation? James B. Dent Department of Physics, University of Louisiana at Lafayette, Lafayette, LA 70504, USA, Lawrence M. Krauss Department of Physics and School of Earth and Space Exploration, Arizona State University, Tempe, AZ 85287, USA, and Mount Stromlo Observatory, Research School of Astronomy and Astrophysics, Australian National University, Weston, ACT, Australia, 2611 Harsh Mathur Department of Physics, Case Western Reserve University. Cleveland. Ohio 44106-7079 The surprisingly large value of r, the ratio of power in tensor to scalar density perturbations in the CMB reported by the BICEP2 Collaboration provides strong evidence for Inflation at the CUT scale. In order to provide compelling evidence, other possible sources of the signal need to be ruled out. While the Inflationary signal remains the best motivated source, the current measurement unfortunately still allows for the poodbility that a comparable gravitational wave background might result from a self ordering scalar field transition that takes place later at somewhat lower energy. However even marginally improved limits on the possible isocurvature contribution to CRIB anistropies could rule out this possibility, and essentially all other sources of the observed signal other than Inflation. The recent claimed observation of primordial gravita- plications (i.e. quantization of gravity (11]). tional waves [1] provides a dramatic new empirical win- In the following we assume inflation occurs, and pro- dow on the early universe. In particular, it provides the vides the measured adiabatic scalar density fluctua- opportunity, in principle, to definitively test the inflation- tions inferred from CMB measurements (because that ary paradigm[2, 3], and to explore the specific physics of is strongly suggested by the data), but that a SOSF inflationary models. However, while there is little doubt phase transition occurs after inflation, producing a grav- that inflation at the Grand Unified Scale is the best mo- itational wave signature that might overwhelm the infla- tivated source of such primordial waves (e.g. [4-7], it tionary signal. is important to demonstrate that other possible sources Let S, and Ti denote the scalar and tensor power gen- cannot account for the current BICEP2 data before def- erated by inflation and Sc, and Tv, the same quanti- initely claiming Inflation has been proved. ties for the self-ordered scalar field. Out of these four A surprisingly large value of r, the ratio of power in quantities one can form several ratios of interest: (i) tensor modes to scalar density perturbations provides a Teff = (71+TO1(51+4) is the tensor to scalar ratio in- challenge for other possible primordial sources, as such corporating both sources that has just been observed to sources would have to generate gravitational waves effi- have a central value of 0.2. (ii) The self-ordering scalar ciently without altering the observed adiabatic density field produces isocurvature scalar fluctuations whereas fluctuations that are so consistent with inflationary pre- inflation produces adiabatic ones. Measurements of the dictions. Here we explore to what extent that challenge temperature anisotropies constrain the isocurvature frac- might rule out other possibilities. tion x = Sv,/(S, + Sy) to lie in the range 0 < x < 0.09 We have previously explored a relatively generic pos- (12]. (iii) r n =T.1Sp, the tensor-to-scalar ratio for the sible competing source of a scale invariant spectrum of SOSF case, can be calculated within the self-ordering tensor modes [8 10], a simple self ordering scalar field scalar field model using the scalar power spectrum de- (SOSF) in the early universe, and frankly had hoped that scribed in (13] along with the tensor power given in [9, 10], the BICEP2 observation would rule out this possibility, and is found to be 2.34 (iv) f =TST„ the ratio of the thus allowing a cleaner interpretation of the the existing tensor contributions from the SOSF mechanism to that data in terms of inflation. As we describe here unfortu- produced by inflation, is given by (140/N)(VSV) [9, 10] nately the measured value of r falls just short of ruling where N denotes the number of components of the self- out this other source as the dominant contribution of the ordering scalar field (presumed to be large and definitely observed effect. Nevertheless, as we also show, reducing greater than three), V„, is the symmetry breaking scale for the bound on any possible isocurvature component of the the self-ordering field and V, is the scale of inflation. We scalar power spectrum can rule out this possibility, and need V, < Vi to ensure that symmetry breaking occurs therefore any likely candidate source after inflation that after inflation (otherwise evidence of it would be oblit- produces gravitational waves. This would then imply erated by inflation). This inequality constrains the ratio the BICEP2 result definitely reflects gravitational waves J. (v) The tensor to scalar ratio for inflation n = Ti/Si from inflation, with all of the exciting concomitant int- is the quantity of interest for inflationary models. In the EFTA_R1_02123537 EFTA02710829  2 absence of the self-ordering scalar fields, r, is equal to 0.2 the measured quantity reff, but the present measurement currently allows r, to have a considerably lower value if self-ordering scalar fields dominate the observed signal. A priori, this need not have been the case. Since only 0 three of these ratios are independent, but there are now constraints on four of them, in principle, the data is capa- ble of ruling out the existence of self-ordering scalar fields as a source. To explicitly determine the constraints we express f in terms of reff, x and r y 0 0 0.04 0.06 0.08 xr„ X - r ag — rr y, (1) FIG. 2: The inflationary tensor-to-scalar ratio, r, as a func- Fig.1 shows a plot off as a function of x reveals that f tion of the isocurvature fraction, x. grows monotonically with x, diverging at x„,, = refry, Pt. 0.085. This cm I esponds to a situation where the SOSF contribution essentially accounts for all of the observed BICEP2 polarization, and therefore contributes a frac- rather than 0 < x < xec. Here tion 0.2/2.34 of the (isocurvature) power in scalar density /max perturbations. Xinsix ) ro c , (2) Since zoo is less than the maximum iso-curvature ra- + tio compatible with the temperature anisotropy data we obtained by inverting eq (1) and setting f -> f,„.„. We arrive at the disappointing conclusion that the new mea- estimate /num •SI 35 by taking N = 4, and setting lc = V1 surement of ref does not additionally constraint self- leading to Xmax PS 0.083. ordering scalar fields. Had ref been larger, the isocurva- Finally for completeness we display the inflationary Lure contribution of SOSF to scalar density perturbations tensor to scalar ratio r1 that may be inferred from the would have to have been larger to account for the entire data as a function of the isocurvature fraction of scalar tensor signal, and existing constraints on this contribu- density perturbations induced by SOSF. This allows a tion would have therefore constrained f, and thereby the quantitative estimate of how future constraints on this symmetry breaking scale, Vim. fraction can then allow one to infer the fraction of the While this is disappointing, it is cause for hope. A BICEP2 signal that must result from Inflation. small improvement on the iso-curvature fraction in CMB Fig.2 shows a plot of r, as a function of x over its al- temperature fluctuations would imply that SOSF cannot lowed range. As can be seen, if the current upper limit of give the full measured contribution to rot and therefore 0.09 is reduced by a factor about 2, then the inflationary the signal from inflation is observable in the data. Alter- contribution must dominate. However, even a reduction natively a non-zero measured isocurvature fraction might by only 20% or so would imply a clear non-zero inflation- be suggestive that an SOSF has occurred and contributes ary component to the observed BICEP2 signal to the BICEP2 signal. NVItile it is perhaps frustrating that the current ob- servation cannot unambiguously rule out this toy model straw man as a source of gravitational waves that could 30 polarize the CMB signal as observed by BICEP2. How- ever, as we have described, we are at the threshold of 20 being able to argue that Inflation unambiguously pro- vides at the very least a non-zero component of the sig- nal. Note that because the scale of inflation varies as the 10 fourth root of r, the scale of inflation will remain essen- tially identical to the Grand Unified Scale independent of whether it contributes all, or only a fraction of the 0.02 0.04 0.06 0.08 observed polarization signal. x We also note that the current analysis has not in- cluded the possible contribution from vector modes due to SOSF. However since such modes are known to con- FIG. 1: Plot of f, the ratio of tensor contributions from SOSF to those of inflation as a function of the isocurvature fraction, tribute roughly equally to scalar and tensor modes in the x. CMB it should not significantly affect ratios, although it would need to be calculated and included in a more complete future quantitative analysis. Note f must lie below a tnaxinnun value, f aax, so x Finally we note that while current data cannot defini- is actually constrained to lie in the range 0 < x < x,„„„ tively rule out a SOSF transition as the source of gravita- EFTA_R1_02123538 EFTA02710830  3 tional waves, it nevertheless does imply that the source flation is responsible for the entire BICEP2 signal, even for such waves is at, or near the Grand Unified Scale. though existing data from cosmology is strongly sugges- Thus, it allows an exploration of physics at a scale far tive that it does. larger than we can currently constrain at terrestrial ex- periments. This will be very important for constraining We acknowledge discussions with Kate Jones-Smith physics beyond the standard model, whether or not in- and Paul J. Steinhardt at an early stage of this work. 111 BICEP2 Collaboration (P.A.R. Me et al.), [9] K. Jones-Smith, L.M. Krauss, and H. Mathur, arXiv:1403.3985 (astro-ph.CO]. 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