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We study how well perturbative forward modeling can constrain cosmologicalparameters compared to conventional analyses. We exploit the fact that inperturbation theory the field-level posterior can be computed analytically inthe limit of small noise. In the idealized case where the only relevantparameter for the nonlinear evolution is the nonlinear scale, we argue thatinformation content in this posterior is the same as in the $n$-pointcorrelation functions computed at the same perturbative order. In the realuniverse other parameters can be important, and there are possibly enhancedeffects due to nonlinear interactions of long and short wavelength fluctuationsthat can either degrade the signal or increase covariance matrices. We identifyseveral different parameters that control these enhancements and show that forsome shapes of the linear power spectrum they can be large. This leads todegradation of constraints in the standard analyses, even though the effectsare not dramatic for a $\Lambda$CDM-like cosmology. The aforementionedlong-short couplings do not affect the field-level inference which remainsoptimal. Finally, we show how in these examples calculation of the perturbativeposterior motivates new estimators that are easier to implement in practicethan the full forward modelling but lead to nearly optimal constraints oncosmological parameters.

Cosmological Information in Perturbative Forward Modeling