Cosmic Star Formation Rate Density

• Cosmic star formation rate density (SFRD) is the rate at which the universe forms stars, expressed as a function of redshift and serving as a key summary statistic for galaxy evolution.
• Multiwavelength measurements—spanning UV, IR, radio, and submillimeter bands—and various modeling approaches reveal tracer-dependent peaks, dust obscuration effects, and differing redshift evolutions.
• Accurate SFRD estimation relies on integrating luminosity functions and direct star formation measurements, with ongoing debates on peak timing and dust corrections influencing cosmological interpretations.

Cosmic star formation rate density (SFRD) is the comoving rate at which the Universe forms stars, usually expressed as a function of redshift or cosmic time. It is a central summary statistic of galaxy evolution because it links luminosity functions, stellar-mass build-up, metal production, dust-obscured activity, and, at the highest redshifts, reionization-era star formation. The canonical multiwavelength synthesis places the maximum of the SFRD near “cosmic noon,” but recent radio, submillimeter, generative-model, tomographic, and cosmological reconstructions show that the precise peak redshift, amplitude, and high-redshift decline remain tracer- and model-dependent (Madau et al., 2014, Deger et al., 24 Sep 2025, Moyses et al., 19 Apr 2026).

1. Definition and mathematical representations

In catalog-based analyses, the SFRD is the sum of galaxy star-formation rates divided by comoving volume. For submillimeter galaxies (SMGs), one explicit estimator is

$$\mathrm{SFRD}_{\mathrm{SMG}}(z)=\frac{1}{V}\sum_{i\in \mathrm{SMGs}} \mathrm{SFR}_i ,$$

while in the generative-model analysis of COSMOS2020 galaxies the redshift-bin estimator is

$$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$

with the sum taken over accepted mock galaxies in bin $b$ (Kumar et al., 31 Jan 2025, Deger et al., 24 Sep 2025).

Luminosity-function methods instead write the SFRD as an integral over a tracer-dependent luminosity function,

$$\mathrm{SFRD}(z)=\int \Phi(L,z)\,\mathrm{SFR}(L)\,d\log_{10}L ,$$

after specifying an observational calibration from luminosity to star-formation rate. This is the standard construction in radio, UV, IR, and H$\alpha$ work (Wang et al., 2023, Vlugt et al., 2022, Katsianis et al., 2016).

Several analytic forms are used to summarize the redshift evolution. A widely adopted empirical fit is the Madau–Dickinson form,

$$\psi(z)=0.015\,\frac{(1+z)^{2.7}}{1+\left[(1+z)/2.9\right]^{5.6}} \quad \left[\mathrm{M}_\odot\,\mathrm{yr}^{-1}\,\mathrm{Mpc}^{-3}\right] ,$$

which was designed to capture the rise, turnover, and late decline of the global history (Madau et al., 2014). A more physically motivated cosmological fit uses the Hernquist–Springel prescription,

$$\dot{\rho}_\star(z)=\dot{\rho}_{\star,0}\, \frac{\chi^2}{1+\alpha(\chi-1)^3\exp(\beta\chi^{7/4})}, \qquad \chi=\left(\frac{H(z)}{H_0}\right)^{2/3},$$

thereby making the SFRD explicitly cosmology-dependent (Moyses et al., 19 Apr 2026). A separate phenomenological study argues that the observed CSFRD can be described by only two parameters and a function that has the form of a Gamma distribution,

$$\mathrm{CSFRD}(t)=\frac{b^a}{\Gamma(a)}\,t^{a-1}e^{-bt},$$

with the parameters connected to the star formation rate depletion time and cosmic baryonic gas density (Katsianis et al., 2021).

2. Measurement strategies across wavelengths and methodologies

The observational route to the SFRD depends on tracer physics. UV emission directly traces young, massive stars, but dust attenuation is a first-order systematic. IR emission is an excellent probe of obscured star formation, especially in massive dusty systems, while H$\alpha$ provides an emission-line census of lower-SFR galaxies where mild obscuration occurs. Radio wavelengths offer a dust-unbiased tracer of the total SFR, provided AGN contamination and the IR–radio calibration are handled consistently (Katsianis et al., 2016, Wang et al., 2023, Novak et al., 2017).

Classical SFRD compilations are built by integrating dust-corrected UV and IR luminosity functions over redshift (Madau et al., 2014). Radio studies refine this strategy by fitting analytic radio luminosity functions directly to source catalogs with completeness corrections and AGN rejection or subtraction. In the VLA-COSMOS and GOODS-N analyses, the radio luminosity function is fit with modified Schechter or LADE-type models, and the SFRD follows from integrating the fitted function after applying a redshift-dependent IR–radio conversion (Wang et al., 2023, Enia et al., 2022). One recent radio study emphasizes that fitting the luminosity function directly to the data, rather than to binned $1/V_{\max}$ points, reduces bias in the inferred SFRD (Wang et al., 2023).

Other methods depart from luminosity-function fitting altogether. The pop-cosmos framework trains a score-based diffusion model on 26-band photometry of $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$0 COSMOS2020 galaxies, generates mock catalogs with 16 SPS parameters, and computes the SFRD by directly integrating individual galaxy SFRs. The stated advantage is that this approach avoids constructing and fitting a parametric luminosity function and evades extrapolation below observational limits, dust corrections, and SFR conversion factors associated with luminosity-function methods (Deger et al., 24 Sep 2025). At low redshift, fossil-record analyses reconstruct star-formation histories of nearby galaxies with delayed-$$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$1 models and infer the cosmic SFRD, sSFR, and stellar-mass density from spatially resolved stellar populations (Fernández et al., 2018).

Tomographic and intensity-mapping methods extend the observable. Cross-correlation of the cosmic infrared background with KiDS galaxy samples was detected at $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$2 and modeled with a halo framework to recover the SFRD up to $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$3, or to $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$4 when external SFRD measurements are added (Yan et al., 2022). CO intensity mapping with one-point $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$5 statistics was proposed as a high-redshift route to the SFRD at $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$6–$$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$7; for pessimistic model uncertainty the forecast error is of order $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$8, while improved CO–SFR calibration yields roughly $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$9–$b$0 precision (Breysse et al., 2015).

3. Global evolutionary history and the location of the peak

The canonical synthesis by Madau and Dickinson places the SFRD peak approximately $b$1 Gyr after the Big Bang, at $b$2, followed by an exponential decline with an e-folding timescale of $b$3 Gyr. In that framework, half of the stellar mass observed today was formed before $b$4, about $b$5 formed before the SFRD peak, another $b$6 formed after $b$7, and less than $b$8 of today’s stars formed during the epoch of reionization (Madau et al., 2014).

Recent measurements do not yield a single unique peak. The pop-cosmos generative reconstruction finds that the SFRD peaks at $b$9 with peak value $$\mathrm{SFRD}(z)=\int \Phi(L,z)\,\mathrm{SFR}(L)\,d\log_{10}L ,$$0, about $$\mathrm{SFRD}(z)=\int \Phi(L,z)\,\mathrm{SFR}(L)\,d\log_{10}L ,$$1 later than Madau and Dickinson, with a broader, later maximum and a flatter high-redshift decline (Deger et al., 24 Sep 2025). The tomographic CIB–galaxy analysis, when combined with external SFRD measurements, yields a peak SFRD of $$\mathrm{SFRD}(z)=\int \Phi(L,z)\,\mathrm{SFR}(L)\,d\log_{10}L ,$$2 at $$\mathrm{SFRD}(z)=\int \Phi(L,z)\,\mathrm{SFR}(L)\,d\log_{10}L ,$$3, corresponding to a lookback time of $$\mathrm{SFRD}(z)=\int \Phi(L,z)\,\mathrm{SFR}(L)\,d\log_{10}L ,$$4 Gyr (Yan et al., 2022).

Radio reconstructions tend to place the maximum somewhat later than the canonical UV+IR fit or to broaden it into a plateau, but not uniformly. The COSMOS-XS analysis finds that the radio-based SFRD rises steeply out to $$\mathrm{SFRD}(z)=\int \Phi(L,z)\,\mathrm{SFR}(L)\,d\log_{10}L ,$$5 and then declines more rapidly than previous radio-based estimates (Vlugt et al., 2022). A separate radio luminosity-function study concludes that the SFRD peaks between $$\mathrm{SFRD}(z)=\int \Phi(L,z)\,\mathrm{SFR}(L)\,d\log_{10}L ,$$6 and $$\mathrm{SFRD}(z)=\int \Phi(L,z)\,\mathrm{SFR}(L)\,d\log_{10}L ,$$7 and falls more rapidly toward high redshift once density evolution is included (Wang et al., 2023). By contrast, the GOODS-N radio-selected analysis reports a rise up to $$\mathrm{SFRD}(z)=\int \Phi(L,z)\,\mathrm{SFR}(L)\,d\log_{10}L ,$$8 and then an almost flat plateau up to $$\mathrm{SFRD}(z)=\int \Phi(L,z)\,\mathrm{SFR}(L)\,d\log_{10}L ,$$9 (Enia et al., 2022).

At the modeling end, cosmological reconstruction with SFRD data compiled over $\alpha$0 gives a robust peak at

$\alpha$1

within $\alpha$2CDM, with similar values in $\alpha$3CDM (Moyses et al., 19 Apr 2026). Taken together, these results indicate that the existence of a broad “cosmic noon” is secure, whereas the precise peak location and width remain sensitive to tracer choice, dust treatment, luminosity-function parameterization, and the adopted mapping between astrophysical and cosmological parameters.

4. Dust-obscured star formation and high-redshift revisions

A major current issue is how much of the SFRD is missed by rest-UV selection. The ASPIRE JWST+ALMA program provides a spectroscopically complete census of dusty star-forming galaxies at $\alpha$4–$\alpha$5 over $\alpha$6 arcmin$\alpha$7 and measures

$\alpha$8

It further concludes that the majority, $\alpha$9, of cosmic star formation at $$\psi(z)=0.015\,\frac{(1+z)^{2.7}}{1+\left[(1+z)/2.9\right]^{5.6}} \quad \left[\mathrm{M}_\odot\,\mathrm{yr}^{-1}\,\mathrm{Mpc}^{-3}\right] ,$$0 is still obscured by dust, and that the IR luminosity function flattens toward the faint end with slope $$\psi(z)=0.015\,\frac{(1+z)^{2.7}}{1+\left[(1+z)/2.9\right]^{5.6}} \quad \left[\mathrm{M}_\odot\,\mathrm{yr}^{-1}\,\mathrm{Mpc}^{-3}\right] ,$$1 (Sun et al., 2024).

At even earlier times, the REBELS ALMA survey at $$\psi(z)=0.015\,\frac{(1+z)^{2.7}}{1+\left[(1+z)/2.9\right]^{5.6}} \quad \left[\mathrm{M}_\odot\,\mathrm{yr}^{-1}\,\mathrm{Mpc}^{-3}\right] ,$$2 infers a mass-dependent obscured fraction $$\psi(z)=0.015\,\frac{(1+z)^{2.7}}{1+\left[(1+z)/2.9\right]^{5.6}} \quad \left[\mathrm{M}_\odot\,\mathrm{yr}^{-1}\,\mathrm{Mpc}^{-3}\right] ,$$3–$$\psi(z)=0.015\,\frac{(1+z)^{2.7}}{1+\left[(1+z)/2.9\right]^{5.6}} \quad \left[\mathrm{M}_\odot\,\mathrm{yr}^{-1}\,\mathrm{Mpc}^{-3}\right] ,$$4 for galaxies with $$\psi(z)=0.015\,\frac{(1+z)^{2.7}}{1+\left[(1+z)/2.9\right]^{5.6}} \quad \left[\mathrm{M}_\odot\,\mathrm{yr}^{-1}\,\mathrm{Mpc}^{-3}\right] ,$$5–$$\psi(z)=0.015\,\frac{(1+z)^{2.7}}{1+\left[(1+z)/2.9\right]^{5.6}} \quad \left[\mathrm{M}_\odot\,\mathrm{yr}^{-1}\,\mathrm{Mpc}^{-3}\right] ,$$6 and an obscured cosmic SFRD

$$\psi(z)=0.015\,\frac{(1+z)^{2.7}}{1+\left[(1+z)/2.9\right]^{5.6}} \quad \left[\mathrm{M}_\odot\,\mathrm{yr}^{-1}\,\mathrm{Mpc}^{-3}\right] ,$$7

with a lower limit of $$\psi(z)=0.015\,\frac{(1+z)^{2.7}}{1+\left[(1+z)/2.9\right]^{5.6}} \quad \left[\mathrm{M}_\odot\,\mathrm{yr}^{-1}\,\mathrm{Mpc}^{-3}\right] ,$$8. The survey argues that dust-obscured star formation still contributes $$\psi(z)=0.015\,\frac{(1+z)^{2.7}}{1+\left[(1+z)/2.9\right]^{5.6}} \quad \left[\mathrm{M}_\odot\,\mathrm{yr}^{-1}\,\mathrm{Mpc}^{-3}\right] ,$$9 at $$\dot{\rho}_\star(z)=\dot{\rho}_{\star,0}\, \frac{\chi^2}{1+\alpha(\chi-1)^3\exp(\beta\chi^{7/4})}, \qquad \chi=\left(\frac{H(z)}{H_0}\right)^{2/3},$$0 (Algera et al., 2022).

Radio and submillimeter surveys also imply a substantial obscured component at high redshift. The VLA-COSMOS 3 GHz analysis finds evidence that UV-based SFRD estimates at $$\dot{\rho}_\star(z)=\dot{\rho}_{\star,0}\, \frac{\chi^2}{1+\alpha(\chi-1)^3\exp(\beta\chi^{7/4})}, \qquad \chi=\left(\frac{H(z)}{H_0}\right)^{2/3},$$1 underestimate the true SFRD by $$\dot{\rho}_\star(z)=\dot{\rho}_{\star,0}\, \frac{\chi^2}{1+\alpha(\chi-1)^3\exp(\beta\chi^{7/4})}, \qquad \chi=\left(\frac{H(z)}{H_0}\right)^{2/3},$$2–$$\dot{\rho}_\star(z)=\dot{\rho}_{\star,0}\, \frac{\chi^2}{1+\alpha(\chi-1)^3\exp(\beta\chi^{7/4})}, \qquad \chi=\left(\frac{H(z)}{H_0}\right)^{2/3},$$3 because of appreciable star formation in highly dust-obscured galaxies (Novak et al., 2017). The COSMOS-XS study pushes this discrepancy further at matched luminosity limits, reporting that the radio-based SFRD exceeds the UV-based, dust-corrected SFRD by approximately $$\dot{\rho}_\star(z)=\dot{\rho}_{\star,0}\, \frac{\chi^2}{1+\alpha(\chi-1)^3\exp(\beta\chi^{7/4})}, \qquad \chi=\left(\frac{H(z)}{H_0}\right)^{2/3},$$4 dex for $$\dot{\rho}_\star(z)=\dot{\rho}_{\star,0}\, \frac{\chi^2}{1+\alpha(\chi-1)^3\exp(\beta\chi^{7/4})}, \qquad \chi=\left(\frac{H(z)}{H_0}\right)^{2/3},$$5 (Vlugt et al., 2022).

The dust problem is not one-sided. A semi-analytic reassessment of UV-derived CSFRD argues that standard dust obscuration corrections and UV-to-SFR conversions can overestimate the CSFRD by $$\dot{\rho}_\star(z)=\dot{\rho}_{\star,0}\, \frac{\chi^2}{1+\alpha(\chi-1)^3\exp(\beta\chi^{7/4})}, \qquad \chi=\left(\frac{H(z)}{H_0}\right)^{2/3},$$6–$$\dot{\rho}_\star(z)=\dot{\rho}_{\star,0}\, \frac{\chi^2}{1+\alpha(\chi-1)^3\exp(\beta\chi^{7/4})}, \qquad \chi=\left(\frac{H(z)}{H_0}\right)^{2/3},$$7 dex and $$\dot{\rho}_\star(z)=\dot{\rho}_{\star,0}\, \frac{\chi^2}{1+\alpha(\chi-1)^3\exp(\beta\chi^{7/4})}, \qquad \chi=\left(\frac{H(z)}{H_0}\right)^{2/3},$$8–$$\dot{\rho}_\star(z)=\dot{\rho}_{\star,0}\, \frac{\chi^2}{1+\alpha(\chi-1)^3\exp(\beta\chi^{7/4})}, \qquad \chi=\left(\frac{H(z)}{H_0}\right)^{2/3},$$9 dex, respectively, compared with the model’s intrinsic values, and presents new redshift-dependent calibrations for both effects (Kobayashi et al., 2012). Taken together, these results indicate that discrepancies among high-redshift SFRD determinations arise from both genuinely obscured populations that UV surveys miss and from biases introduced when dust and SFR calibrations are assumed to be redshift-invariant.

5. Decomposition by galaxy mass, morphology, halo mass, and submillimeter population

The SFRD can be resolved by stellar mass, morphology, galactic radius, or halo mass. At $$\mathrm{CSFRD}(t)=\frac{b^a}{\Gamma(a)}\,t^{a-1}e^{-bt},$$0, the ROLES survey finds that the shape of the SFRD as a function of stellar mass does not evolve between $$\mathrm{CSFRD}(t)=\frac{b^a}{\Gamma(a)}\,t^{a-1}e^{-bt},$$1 and $$\mathrm{CSFRD}(t)=\frac{b^a}{\Gamma(a)}\,t^{a-1}e^{-bt},$$2, even though the normalization declines by a factor of $$\mathrm{CSFRD}(t)=\frac{b^a}{\Gamma(a)}\,t^{a-1}e^{-bt},$$3 in the corrected [OII]-based estimate and by $$\mathrm{CSFRD}(t)=\frac{b^a}{\Gamma(a)}\,t^{a-1}e^{-bt},$$4 in the UV-based estimate (Gilbank et al., 2010). In the nearby Universe, MUSE and GAMA extend the SFRD–mass relation down to $$\mathrm{CSFRD}(t)=\frac{b^a}{\Gamma(a)}\,t^{a-1}e^{-bt},$$5 and find a constant low-mass slope in log SFRD versus log stellar mass, with no turn-over in the galaxy stellar mass function (Murrell et al., 2024).

Spatially resolved fossil-record work adds a structural dimension. In CALIFA, most star formation at $$\mathrm{CSFRD}(t)=\frac{b^a}{\Gamma(a)}\,t^{a-1}e^{-bt},$$6 takes place in the outer regions of late spiral galaxies, whereas at $$\mathrm{CSFRD}(t)=\frac{b^a}{\Gamma(a)}\,t^{a-1}e^{-bt},$$7 the inner regions of the progenitors of current E and S0 galaxies are the major contributors to the SFRD. The same analysis finds that the inner regions are the major contributor to stellar-mass density at $$\mathrm{CSFRD}(t)=\frac{b^a}{\Gamma(a)}\,t^{a-1}e^{-bt},$$8, consistent with inside-out growth (Fernández et al., 2018).

Halo-based analyses assign the SFRD to characteristic environments. Tomographic CIB–galaxy cross-correlation yields a best-fit maximum star formation efficiency of $$\mathrm{CSFRD}(t)=\frac{b^a}{\Gamma(a)}\,t^{a-1}e^{-bt},$$9 at $\alpha$0, shifting to $\alpha$1 when external SFRD measurements are included (Yan et al., 2022). This places the most efficient star formation in halos near $\alpha$2.

Submillimeter-selected systems provide a direct population-level contribution to the SFRD around the peak epoch. In cosmological simulations calibrated to reproduce observed SMG counts and redshift distributions, SMGs with $\alpha$3 contribute up to $\alpha$4 of the total cosmic SFRD at $\alpha$5 in FLAMINGO. The same study finds that the abundance of SMGs rises from $\alpha$6 to $\alpha$7 and then declines sharply, and that sources with $\alpha$8 are exclusively starburst galaxies. For the TolTEC Ultra Deep Survey over $\alpha$9 deg$1/V_{\max}$0, the forecast is $1/V_{\max}$1 detections at $1/V_{\max}$2 mm and about $1/V_{\max}$3 of the cosmic SFRD captured at $1/V_{\max}$4 (Kumar et al., 31 Jan 2025).

6. Physical interpretations from simulations and semi-analytic models

Semi-analytic and hydrodynamic models generally interpret the SFRD as the convolution of galaxy star-formation histories with the growth of the halo population. A simple semi-analytic treatment writes the SFRD as the sum over galaxies of different masses and types, weighted by the evolving number density of dark matter halos $1/V_{\max}$5. In that framework, the “time-delayed” star-formation history,

$1/V_{\max}$6

is essential for reproducing the broad asymmetric shape of the observed SFRD, while artificially fixing $1/V_{\max}$7 destroys the agreement. Moderate, prolonged feedback and winds modulate the normalization, but the principal drivers are the evolving halo mass function and the delayed shape of galaxy star-formation histories (Chiosi et al., 2017).

Cosmological SPH simulations refine this picture by making the feedback prescription explicit. A comparison of UV, IR, and H$1/V_{\max}$8 SFR functions with P-GADGET3(XXL) simulations at $1/V_{\max}$9–$$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$00 shows that AGN feedback decreases the simulated CSFRD at $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$01 but is not sufficient to reproduce the observed evolution at higher redshift. The best overall match comes from variable galactic winds that are efficient at decreasing the SFRs of low-mass objects at high redshift and become less efficient with time (Katsianis et al., 2016).

Submillimeter galaxy modeling further reveals that not all large-volume simulations reproduce the same obscured contribution. When parametric radiative-transfer-based flux prescriptions are applied to EAGLE, IllustrisTNG, and FLAMINGO, only FLAMINGO reproduces the observed SMG number counts and redshift distributions without requiring a top-heavy IMF; EAGLE and IllustrisTNG show a deficit of bright SMGs and a lower SFRD at $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$02–$$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$03 (Kumar et al., 31 Jan 2025). This emphasizes that reproducing the global SFRD is not equivalent to reproducing the distribution of dust-obscured star formation across galaxy populations.

7. Cosmological applications and persistent controversies

The SFRD is increasingly treated as a cosmological observable rather than only a galaxy-evolution summary. A recent compilation over $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$04 fits SFRD jointly with cosmological parameters in $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$05CDM and $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$06CDM. In that analysis, SFRD combined with BBN alone gives $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$07 km\,s$$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$08\,Mpc$$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$09, while adding DESI-DR2 BAO yields $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$10 km\,s$$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$11\,Mpc$$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$12; joint analyses reduce uncertainties in astrophysical parameters by $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$13–$$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$14 and preserve a robust $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$15 near $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$16 (Moyses et al., 19 Apr 2026).

At the same time, fundamental methodological disagreements remain. One study argues that UV-corrected and IR-derived star-formation-rate functions are described by different distributions—Schechter for UV$$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$17 and double power law for IR—and compare differently with the stellar-mass density evolution, even though both indicate a plateau rather than a sharp peak at $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$18–$$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$19 (Katsianis et al., 2021). Radio luminosity-function modeling reaches a related conclusion: pure luminosity evolution cannot describe the high-redshift radio LF, whereas luminosity+density evolution is genuinely indispensable, and the adopted FIR–radio calibration can shift the SFRD by factors of $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$20 (Wang et al., 2023). A stellar-mass-selected radio analysis likewise finds that beyond $$\Psi_b=\frac{N f_b}{V_{{\rm co},b}}\,\frac{1}{N_b}\sum_{n=1}^{N_b}\psi_n ,$$21 the inferred decline of the SFRD depends crucially on whether the IR–radio correlation is allowed to evolve (Malefahlo et al., 2020).

The present state of the field is therefore one of broad agreement on the existence of a cosmic noon, but continuing disagreement on its exact timing, on the magnitude of the obscured component at high redshift, and on the appropriate functional form for luminosity-function evolution and luminosity-to-SFR conversion. These disagreements are not peripheral: they determine whether the SFRD is interpreted primarily as a tracer of dust-hidden star formation, as a convolution of halo growth and feedback-regulated star formation, or as a complementary probe of background cosmology.