Colliders and ghosts: Constraining inflation with the parity-odd galaxy four-point function

Could new physics break the mirror symmetry of the Universe? Utilizing recent measurements of the parity-odd four-point correlation function of BOSS galaxies, we probe the physics of inflation by placing constraints on the amplitude of a number of parity-violating models. Within canonical models of (single-field, slow-roll) inflation, no parity asymmetry can occur; however, it has recently been shown that breaking of the standard assumptions can lead to parity violation within the effective field theory of inflation (EFTI). In particular, we consider the ghost condensate and cosmological collider scenarios—the former for the leading and subleading operators in the EFTI and the latter for different values of mass and speed of an exchanged spin-1 particle—for a total of 18 models. Each instance yields a definite prediction for the inflationary trispectrum, which we convert to a late-time galaxy correlator prediction (through a highly nontrivial calculation) and constrain using the observed data. We find no evidence for inflationary parity violation (with each of the 18 models having significances below $2\sigma$), and place the first constraints on the relevant coupling strengths, at a level comparable with the theoretical perturbativity bounds. This is also the first time cosmological collider signatures have directly been searched for in observational data. We further show that possible secondary parity-violating signatures in galaxy clustering can be systematically described within the effective field theory of large-scale structure. We argue that these late-time contributions are subdominant compared to the primordial parity-odd signal for a vast region of parameter space. In summary, the results of this paper disfavor the notion that the recent hints of parity violation observed in the distribution of galaxies are due to new physics.

Figure 1

Comparison of the observed galaxy four-point correlation function, ${\zeta }_{{\ell }_1{\ell }_2{\ell }_3}(r_1,r_2,r_3)$ (black points), with two models of the theoretical 4PCF, assuming ghost condensate (black lines) and cosmological collider (colored lines) inflation. We assume fiducial values of $A^{(M_{\mathrm{PO}})}=100A^{({\mathrm{\Lambda }}_{\mathrm{PO}}^2)}={10}^{-10}$ and $A^{({\lambda }_1{\lambda }_3)}={10}^{19}({\mathrm{\Delta }}_{\zeta }^2{)}^4{c}_s^4\sin \pi (\nu +\frac{1}{2})$ for visibility and consider a variety of values of the sound speed $c_s$ and mass $\nu$ in the latter case, indicated by the captions. The second through fifth panels show the correlators for a selection of values of ${\ell }_1$, ${\ell }_2$, ${\ell }_3$ (indicated by the title), with the $x$ axis giving the radial bins, collapsed into one dimension. The first panel shows the values of the radial bin centers corresponding to each one-dimensional bin center. Here, we utilize data from the BOSS CMASS NGC region, and with error bars obtained from the patchy simulations (noting that the data is highly correlated). Notably, the theoretical models have strong (and different) dependence on the multiplet, which the MCMC analysis shows to be broadly inconsistent with the data. Constraints on the model amplitudes are given in Tables 1 and 2.

Figure 2

Constraints on the amplitude of parity violation in the ghost condensate inflationary model, from the leading (left) and subleading (right) EFTI diagrams. We show results both from the mean of 2048 patchy mocks (blue) and the BOSS data (red), constraining both $A^{(M_{\mathrm{PO}})},A^{({\mathrm{\Lambda }}_{\mathrm{PO}}^2)}$ and the corresponding physical parameters, as shown in the title. The $1\sigma$ constraints are shown in Table 1, and correspond to the combinations ${\mathrm{\Lambda }}^5{H}^{1/2}{M}_{\mathrm{PO}}^{-1}{\tilde{\mathrm{\Lambda }}}^{-9/2}=(3.1\pm 2.1)\times {10}^{10}$ and ${\mathrm{\Lambda }}^5{H}^{3/2}{\mathrm{\Lambda }}_{\mathrm{PO}}^{-2}{\tilde{\mathrm{\Lambda }}}^{-9/2}=(-1.5\pm 8.1)\times {10}^8$.

Figure 3

As Fig. 2, but constraining the amplitude of parity violation in the cosmological collider inflationary model, for a massive spin-1 particle. Here, we use parameters $c_s=1$ and $\nu =1$, i.e. $m_{\sigma }=\sqrt{5}H/2$. The $1\sigma$ constraints are shown in Table 1, and correspond to the combination ${\lambda }_1{\lambda }_3/H=(1.1\pm 1.4)\times {10}^{17}$.