Unveiling dark forces with measurements of the Large Scale Structure of the Universe

Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: We're looking at the paper: "Unveiling dark forces with measurements of the Large Scale Structure of the Universe".

Jocelyn: Here's the gist of the paper. The gist: The study derives constraints on long-range forces acting solely in the dark sector by measuring their imprints on the Large Scale Structure (LSS) of the Universe using combinations of Planck and BOSS data, leading to a forecast that future surveys will improve current bounds by an order of magnitude Theoretical Framework for Long-Range Forces A long-range dark force can be mediated by an ultralight scalar field with mass mφ = λ−1φ < H0 ≈ 10−33 eV and trilinear coupling to the DM field χ, Lint = − κφχ2 Introducing the dimensionless field s = G 1/2 s φ, with effective constant Gs ≡ κ 2/m4 χ, the model Lagrangian becomes −2L ⊃ (∂χ)2 + m2 χ(s)χ2 + (∂s)2 + m2 φs squared /Gs,(1) The effect of the long-range scalar force can thus be reabsorbed in a space-time dependent mass for DM, mχ(s) = mχ(1 + 2s) 1/2 Radiative corrections induced by DM loops make mφ directly sensitive to the DM mass, so that requiring mφ ≲ H0 bounds the DM mass from above, mχ ≲ (16π/2M2 PlH20 /β) 1/4,(2) In light of the current constraint on β from the CMB, β ≲ 0.01

26: Our analytical results are systematically derived at leading order in the small β expansion Impact on Cosmological Correlators The presence of a scalar long-range force modifies the sub-horizon dynamics in two ways: i) it enhances the growth of the total matter fluctuations; ii) it sources relative density and velocity fluctuations between DM and baryons In the sub-horizon limit k ≫ aH and deep in matter domination, we find that linear level we find δ(1)m (k, a) = D1mδ0(k), with a linear growth factor D1m ≃ 1 + 6/5 εfχ log a/aeq − 181/90 DCDM1m, (6) The overall growth gets enhanced compared to the CDM case at O(β), with a large logarithm boosting this effect even further At O(β) we can take H = 2/τ and a = Cτ squared with C ≡ Ω0 mH20 /4 in Eq.

Vera: (A2) to solve for the scalar field profile, obtaining ¯s−sbareq = − βme sfχ log(τ /τeq), where me s ≡ d log mχ(s)/ds= Via Eq.

Jocelyn: (A3), the decreasing value of ¯s makes the interacting DM χ redshift faster than cold DM by a factor of 2ε log(τ /τeq), where we defined ε ≡ βfχme squared s as in Eq.

Vera: (3) As a consequence, the Hubble parameter in matter domination also receives a log-enhanced correction, H/HCDM = 1 − εfχ log τ /τeq, with ε ≡ βme squared s fχ at leading order in β Constraints from Galaxy Power Spectrum and Bispectrum The observables measured in redshift surveys are correlation functions of the galaxy number density perturbation δg ≡ ng/nbar g − 1, which, at long wavelengths, can be expanded in terms of the matter fields as δg = b1δm + brδr + bθθr + nonlinear terms,(4) In the sub-horizon limit k ≫ aH and deep in matter domination, we find δ(1)g (k, a) = D1m b1+ε5bbr/3 δ0(k), where bbr ≡ br−bθH,(A6) The galaxy power spectrum at tree level reads, retaining only the leading log-enhanced terms, Pg,L(k) ≃ b squared 1 / (1 + 12/5 εfχ log a/aeq PCDM m,L (k), (A11) The overall growth gets enhanced compared to the CDM case at O(β), with a large logarithm boosting this effect even further Forecasts from Future Surveys Our forecasts are based on the 1-loop modeling of the redshift space galaxy power spectrum presented in Ref.

Title and authors: Vera: Moving into the title and authors for this paper, we have Salvatore Bottaro, Emanuele Castorina, Marco Costa, Diego Redigolo and Ennio Salvioni as the authors.

Jocelyn: These are physicists from different institutions across Italy and Canada who are tackling this problem of dark forces in structure formation.

Subrahmanyan: The title itself tells us they are using measurements of the Large Scale Structure of the Universe to try and find these dark forces.

Vera: It’s about looking at galaxy distribution on a large scale, which is what surveys like Planck and BOSS measure, to see if they leave any unique signatures beyond standard gravity.

Jocelyn: The implication here is that cosmology offers an opportunity to test dark matter independently of its interactions with the Standard Model.

Subrahmanyan: Exactly. If we can constrain these forces, it tells us something fundamental about what dark matter is and how it behaves on cosmological scales.

Vera: It’s about using the observed distribution of galaxies to probe physics that isn't covered by our current particle physics models alone.

The paper's summary: Jocelyn: So, to summarize what they found in "Unveiling dark forces with measurements of the Large Scale Structure of the Universe," they are investigating the imprints of long-range dark forces on galaxy distribution.

Vera: They model these forces using an ultralight scalar field and show how this changes the growth of matter fluctuations, enhancing it compared to standard cold dark matter.

Subrahmanyan: The key result here is that at leading order in the small beta expansion, the time dependence is still largely captured by a linear growth factor similar to CDM, modulo some non-log-enhanced subleading terms.

Vera: They show that these new nonlinearities induced by the dark force don't introduce any additional spatial structure and they don't change the infrared behavior of the solution, which simplifies modeling nonlinear dynamics significantly.

Jocelyn: They derive a onedimensional Fisher forecast from this model, estimating the idealized Euclid reach based on real space power spectrum measurements.

Subrahmanyan: The paper finds that at ninety-five percent confidence level from the real space power spectrum, they get a bound of epsilon f chi P g less than one point five times ten to the negative four for k max equal to zero point two seven h Mpc negative one <ref:2309.11496#pg3,from the real space power spectrum>.

Vera: That number is what we use to gauge how sensitive future galaxy surveys like Euclid will be in constraining the dark force strength.

The paper's improvements: Subrahmanyan: The authors suggest a few improvements to the approach, mainly focusing on making it more robust and sensitive.

Jocelyn: They focus on incorporating constraints from both the galaxy power spectrum and the bispectrum to better break degeneracies between cosmological parameters and nuisance parameters.

Vera: That’s important because when you only look at the power spectrum, you can get tangled up with other things that we don't know well.

Subrahmanyan: The paper also points out that including the galaxy bispectrum helps dramatically in better constraining nonlinear biases, which is where those non-log-enhanced subleading terms come into play.

Jocelyn: They also note that extending the perturbative modeling of higher-point correlators, specifically to the galaxy bispectrum, might reach the same level of sensitivity as what we see in the power spectrum analysis.

Vera: And they suggest that beyond just n-point functions, probing directly at the galaxy velocity field with peculiar velocity surveys could enable auxiliary constraints and help isolate those non-log-enhanced EP violations.

Conclusion: Jocelyn: So to wrap up, this paper on "Unveiling dark forces with measurements of the Large Scale Structure of the Universe" suggests that including the galaxy power spectrum as measured by BOSS improves constraints on the dark force strength by a factor of two compared to using only CMB data.

Vera: They reach a bound of beta less than zero point four eight at ninety-five percent confidence level, which is a stronger constraint than what was achieved with just the CMB alone <ref:2309.11496#pg3>.

Subrahmanyan: The final forecast they give for Euclid based on the power spectrum is that beta m epsilon squared s f two chi will be less than one point five times ten to the negative four for a maximum wave number of zero point two seven h Mpc negative one <ref:2309.11496#pg2>.

Jocelyn: They also provide a forecasted bound for the Euclid bispectrum, saying beta m epsilon squared s f two chi will be less than seven point three times ten to the negative four for a maximum wave number of zero point eleven h Mpc negative one <ref:2309.11496#pg3>.

Vera: These numbers show that future surveys could dramatically improve current bounds, and they are pushing the limits on how strong these long-range interactions can be in the dark sector.

Subrahmanyan: It’s exciting because it gives us a clear target for what we should look for when we start looking at these next generation galaxy surveys.

Jocelyn: It certainly points toward more detailed modeling being necessary to fully exploit those future data sets, and that’s the next step in the research.