Cosmic Spectral Energy Distribution (CSED)

• CSED is the Universe’s instantaneous luminosity density spectrum, reflecting star formation, dust attenuation, and AGN activity at fixed redshifts.
• Empirical methods such as band-by-band luminosity functions and panchromatic SED stacking enable precise measurements of the CSED across cosmic time.
• Modeling the CSED links intrinsic and emergent galaxy light to reconstruct the extragalactic background and informs studies of cosmic reionisation.

Searching arXiv for recent and foundational papers on the Cosmic Spectral Energy Distribution (CSED) to ground the article. The Cosmic Spectral Energy Distribution (CSED) is the emissivity spectrum of a representative cosmic volume at a given epoch or redshift. In contemporary usage it is the time-resolved counterpart of the extragalactic background light (EBL): the EBL is the cumulative record of all extragalactic photon production since decoupling, whereas the CSED is the instantaneous spectral output of the Universe at one moment in cosmic history. In that sense the CSED is a volume emissivity, usually written in terms of the comoving spectral emissivity $\epsilon_\nu(z)$ or $j_\nu(z)$, and it functions as a compact summary statistic for cosmic star formation, dust attenuation and reradiation, AGN activity, stellar mass assembly, and the buildup of the optical and infrared backgrounds (Driver, 2021).

1. Definition, formalism, and relation to the EBL

The essential distinction is between an intrinsic production rate and an observed accumulated background. The CSED is the luminosity density spectrum of the Universe at fixed redshift; the EBL is the redshifted and diluted integral of all past CSEDs observed today. This is why the CSED is routinely described as the “instantaneous energy production budget,” while the EBL is a line-of-sight accumulated surface brightness or specific intensity. The integrated galactic light (IGL) is the dominant resolved-object contribution to the EBL, estimated from galaxy and AGN number counts; in the absence of diffuse emission, EBL and IGL would coincide (Driver, 2021).

A second distinction is between intrinsic and emergent spectra. The literature separates a pre-dust attenuation or unattenuated CSED from a post-dust attenuation or attenuated CSED. The former is the stellar radiation before absorption by dust; the latter is the emergent UV/optical/near-IR light after attenuation, supplemented by dust-reprocessed mid/far-IR emission and AGN contributions where included (Andrews et al., 2017).

In standard notation consistent with this usage, the present-day specific intensity of the EBL can be written as

$$I_{\nu_0} = \frac{c}{4\pi} \int_0^\infty \frac{\epsilon_\nu\!\left((1+z)\nu_0,z\right)}{(1+z)\,H(z)}\,dz,$$

with the factor $1+z$ accounting for photon-energy redshifting and time dilation. This relation captures the conceptual point that the observed EBL is built up over time, while the CSED provides the redshift-sliced emissivity history from which that buildup can be reconstructed (Driver, 2021).

2. Empirical construction and observational measurement

Modern CSED work is based on two closely related empirical strategies. One is band-by-band construction from luminosity functions and luminosity densities in a common survey volume. The other is panchromatic stacking of fitted galaxy spectral energy distributions in redshift bins. Both approaches depend on matched multiwavelength photometry and on redshift information sufficient to define representative comoving volumes.

A foundational local result was the homogeneous measurement of the optical-to-near-IR CSED from the combined MGC, SDSS, and UKIDSS LAS datasets. Within a common low-redshift volume and with 100 per cent spectroscopic completeness, the resulting $ugrizYJHK$ luminosity densities produced a smooth local CSED rather than the previously reported optical/NIR discontinuity. The analysis defined the CSED operationally from the per-band luminosity densities $j_\lambda$, converted to a $\nu f_\nu$-type quantity, and showed that when all bands sample the same parent spectroscopic sample and essentially the same cosmic volume, wavelength-dependent discontinuities are much less likely to be survey artifacts (Hill et al., 2010).

This common-volume philosophy was extended in the low-redshift GAMA analysis over $0.013$K$, then combining these with a dust-energy-balance model to obtain a robust description of the nearby Universe from $0.1\,\mu\mathrm{m}$ to $j_\nu(z)$0 mm. That work reported a current intrinsic stellar energy generation rate of

$j_\nu(z)$1

of which

$j_\nu(z)$2

escapes directly into the inter-galactic medium and

$j_\nu(z)$3

is absorbed and reradiated by dust, corresponding to $j_\nu(z)$4 of stellar energy production (Driver et al., 2012).

For redshift evolution, the GAMA and G10/COSMOS analysis constructed the CSED by stacking individual MAGPHYS SED fits in ten redshift intervals from $j_\nu(z)$5 to the present. In that formulation,

$j_\nu(z)$6

where the $j_\nu(z)$7 are incompleteness weights and $j_\nu(z)$8 are the bin comoving volumes. Below $j_\nu(z)$9 the fitted CSEDs were judged credible from 100 nm to 1 mm; above $$I_{\nu_0} = \frac{c}{4\pi} \int_0^\infty \frac{\epsilon_\nu\!\left((1+z)\nu_0,z\right)}{(1+z)\,H(z)}\,dz,$$0 the far-IR increasingly became a mixture of measured and predicted fluxes because of limited Herschel sensitivity (Andrews et al., 2017).

These empirical programs are precisely what made the CSED central to EBL studies. Deep spectroscopic and photometric redshift surveys now allow the EBL to be subdivided into redshift intervals, which in turn allows recovery of the CSED “at any time” (Driver, 2021).

3. Physical components and spectral shaping processes

The CSED is not a single-population observable. In the UV-to-far-IR regime its dominant drivers are star formation, accretion onto black holes, and dust reprocessing. In the high-energy domain the relevant contributors include X-ray binaries, AGN, cooling gas, supernovae, and shocks. At sufficiently high precision, additional channels such as intra-cluster light, intra-group light, intra-halo light, tidal streams, halo gas, diffuse intergalactic emission, reionisation-era sources, and exotic channels such as decaying dark matter or dark-matter/matter interactions also become relevant (Driver, 2021).

Dust is among the most important shaping agents. A recurring result across the literature is that roughly half of the primary optical/UV photons generated by stars and AGN are absorbed by dust and reradiated in the far-IR. The consequence is the familiar suppression of the emergent UV/optical CSED and the appearance of a corresponding far-IR/sub-mm bump. In the language of the infrared background, the Cosmic Infrared Background (CIB) represents about half of the EBL, is emitted in the $$I_{\nu_0} = \frac{c}{4\pi} \int_0^\infty \frac{\epsilon_\nu\!\left((1+z)\nu_0,z\right)}{(1+z)\,H(z)}\,dz,$$1–$$I_{\nu_0} = \frac{c}{4\pi} \int_0^\infty \frac{\epsilon_\nu\!\left((1+z)\nu_0,z\right)}{(1+z)\,H(z)}\,dz,$$2 range, and peaks around $$I_{\nu_0} = \frac{c}{4\pi} \int_0^\infty \frac{\epsilon_\nu\!\left((1+z)\nu_0,z\right)}{(1+z)\,H(z)}\,dz,$$3; it is attributed primarily to dust re-emission from star formation processes, with obscured AGN contributing in a minor way (Béthermin et al., 2011).

Morphological decomposition shows that dust substantially changes the interpretation of the local energy budget. In the GAMA Hubble-type analysis, the observed FUV-to-$$I_{\nu_0} = \frac{c}{4\pi} \int_0^\infty \frac{\epsilon_\nu\!\left((1+z)\nu_0,z\right)}{(1+z)\,H(z)}\,dz,$$4 energy budget is dominated $$I_{\nu_0} = \frac{c}{4\pi} \int_0^\infty \frac{\epsilon_\nu\!\left((1+z)\nu_0,z\right)}{(1+z)\,H(z)}\,dz,$$5 by galaxies with a significant spheroidal component, but after dust correction the balance reverses to approximately $$I_{\nu_0} = \frac{c}{4\pi} \int_0^\infty \frac{\epsilon_\nu\!\left((1+z)\nu_0,z\right)}{(1+z)\,H(z)}\,dz,$$6 in favor of disk-dominated systems; equivalently, the combined disk-dominated populations generate about $$I_{\nu_0} = \frac{c}{4\pi} \int_0^\infty \frac{\epsilon_\nu\!\left((1+z)\nu_0,z\right)}{(1+z)\,H(z)}\,dz,$$7 as much intrinsic energy as spheroid-dominated populations. The same study found that mid-type spirals dominate both the dust-corrected energy production and the local star-formation-rate density, while the observed optical/NIR output appears more spheroid-heavy because star-forming disks are more strongly attenuated (Kelvin et al., 2014).

This distinction between observed and intrinsic CSEDs is central to interpretation. The attenuated CSED traces the energy that actually escapes galaxies into the IGM, whereas the unattenuated CSED is an estimate of what stellar populations produce before internal absorption. The difference between them is not merely a nuisance correction; it is itself a measurement of radiative processing by the interstellar medium.

4. Phenomenological and simulation-based modelling

A major modelling line is the phenomenological framework developed by Driver, Andrews, and collaborators. In this approach the cosmic star-formation history is decomposed into two channels: chaotic clump accretion and major mergers, associated with early spheroid/bulge formation, and cold gas accretion, associated with later disc formation. The model adopts two axioms: AGN activity traces stellar mass growth in spheroids, and material ending up in spheroids today formed predominantly at high redshift. Construction proceeds in five stages: compute the unattenuated CSED from the cosmic star-formation history and metallicity evolution; apply dust attenuation; add far-IR dust emission corresponding to the absorbed energy; add AGN spectra using redshift-dependent AGN luminosity evolution; and integrate the evolving CSED over redshift to obtain the IGL/EBL (Andrews et al., 2017).

The implementation uses Bruzual & Charlot (2003) stellar populations, a Universal Chabrier IMF, Charlot & Fall dust attenuation, Dale et al. IR templates, and two AGN components, unobscured and obscured. The resulting model reproduces observed CSEDs out to $$I_{\nu_0} = \frac{c}{4\pi} \int_0^\infty \frac{\epsilon_\nu\!\left((1+z)\nu_0,z\right)}{(1+z)\,H(z)}\,dz,$$8 and predicts a total energy output peak of

$$I_{\nu_0} = \frac{c}{4\pi} \int_0^\infty \frac{\epsilon_\nu\!\left((1+z)\nu_0,z\right)}{(1+z)\,H(z)}\,dz,$$9

at $1+z$0. It also predicts

$1+z$1

illustrating the near-equality of the optical and infrared backgrounds. In the same framework, the integrated photon escape fraction is defined as

$1+z$2

providing a compact measure of effective attenuation (Andrews et al., 2017).

That phenomenological model also served as a stringent benchmark for semi-analytic work. GALFORM was found to reproduce the shape of the CSED reasonably well at low redshift, but by $1+z$3 its CSED is about $1+z$4 fainter than the empirical CSED, and the predicted IGL is about $1+z$5 fainter, consistent with underprediction of the cosmic star-formation history for $1+z$6 (Andrews et al., 2017).

A complementary route is full hydrodynamical simulation plus radiative transfer. In the EAGLE-SKIRT calculation, the CSED is defined as the total electromagnetic power generated within a cosmological unit volume as a function of wavelength and is expressed as

$1+z$7

For the local Universe, the simulated UV-to-submm CSED was obtained by summing the observed flux densities of every galaxy in the EAGLE-SKIRT database, normalizing by comoving volume and luminosity distance, and averaging the $1+z$8 and $1+z$9 snapshots. The agreement with observed GAMA CSEDs is better than about $ugrizYJHK$0 dex over almost the full UV–submm range at $ugrizYJHK$1, except in the UV where the model overestimates the observed CSED by up to a factor of 2. At higher redshift the agreement deteriorates sharply, with the FIR/submm emissivity underestimated by more than a factor of 5 by $ugrizYJHK$2 (Baes et al., 2019).

5. Evolution with redshift and connection to cosmic backgrounds

Observed CSED evolution from $ugrizYJHK$3 to the present shows a large decline in normalization and a gradual reddening of the unattenuated spectrum. The panchromatic GAMA+G10/COSMOS analysis found that the bolometric energy output of the Universe declines by a factor of roughly four, from

$ugrizYJHK$4

at $ugrizYJHK$5 to

$ugrizYJHK$6

at the current epoch. The unattenuated CSED becomes redder with cosmic time, consistent with increasing mean stellar ages, and dust attenuation decreases over the same interval: at $ugrizYJHK$7 nm the photon escape fraction rises from $ugrizYJHK$8 at $ugrizYJHK$9 to $j_\lambda$0 today, corresponding to a decrease in $j_\lambda$1 of $j_\lambda$2 mag (Andrews et al., 2017).

The relation to the present-day background light is explicit. Integrating the evolving CSED over redshift yields the resolved IGL. In the GAMA+COSMOS study, the measured CSEDs over $j_\lambda$3 account for $j_\lambda$4 of the cosmic optical background and $j_\lambda$5 of the cosmic infrared background as defined from integrated galaxy counts, with total contributions of $j_\lambda$6 and $j_\lambda$7 respectively (Andrews et al., 2017).

At the local end, the low-redshift GAMA result provides a bolometric accounting in which about $j_\lambda$8 of stellar energy is attenuated by dust and reradiated in the far-IR, while the phenomenological model predicts that the present-day COB and CIB are nearly equal. In the broader EBL framework, the CMB dominates the total photon number and energy, while the COB and CIB are each about $j_\lambda$9 of the CMB in energy terms (Driver et al., 2012).

The historical direct-versus-IGL controversy in the optical and near-IR gives the CSED additional importance. Direct EBL estimates had often exceeded IGL values by factors of $\nu f_\nu$0–$\nu f_\nu$1, implying either large diffuse populations or unknown photon-production channels. Recent $\nu f_\nu$2-ray attenuation constraints from H.E.S.S., MAGIC, and Fermi-LAT, together with deep-space probe measurements from Pioneer 10/11 and New Horizons where Zodiacal light is much reduced, instead support the IGL level. The resulting inference is that current IGL measurements represent the full cosmic optical background to within $\nu f_\nu$3 per cent, with more recent work said to have reduced uncertainty on EBL-IGL measurements to below $\nu f_\nu$4 (Driver, 2021).

6. Precision frontier, missing components, and extension to reionisation

A recurring theme in recent CSED work is precision. The programmatic claim is that with upcoming facilities and unified studies from $\nu f_\nu$5-ray to radio wavelengths, it will soon be possible to measure the EBL to within $\nu f_\nu$6 accuracy. At that level, subtle contributors that can be ignored in coarser analyses become unavoidable: reionisation, intra-cluster light, intra-group light, intra-halo light, tidal streams, diffuse halo gas, and any decaying-dark-matter signal. Foreground subtraction systematics, low-surface-brightness incompleteness, fragmentation, over-blending, diffuse light outside standard apertures, and star–galaxy separation then become limiting factors rather than technical details (Driver, 2021).

This same precision agenda frames the long-term interpretation of the CSED. If the EBL is a complete ledger of all extragalactic photons arriving at Earth, then the CSED is the deconvolved ledger, epoch by epoch. The relevant observational infrastructure spans direct and count-based optical/IR programs such as HST, SkySURF, VST KiDS, VISTA VIKING, Euclid, JWST, Roman, LSST, and the proposed Messier mission; redshift-slicing surveys such as DEVILS, WAVES, ESO MOONS, and Subaru PFS; and high-energy or radio facilities such as H.E.S.S., MAGIC, Fermi-LAT, CTA, eROSITA, ASKAP, MeerKAT, LOFAR, and MWA (Driver, 2021).

The precision frontier also reaches into the reionisation problem. A recent extension connects the $\nu f_\nu$7–13.5 cosmic star-formation history and AGN luminosity history to the CSED using ProSpect, then derives the ionising photon emissivity by integrating the spectrum shortward of the Lyman limit,

$\nu f_\nu$8

In that framework, stars alone could have achieved reionisation by $\nu f_\nu$9 with $0.013hybrid model gives best-fit escape fractions of $0.013D'Silva et al., 21 Jul 2025).

The resulting picture is that the CSED has evolved from a local UV-to-near-IR luminosity-density curve into a general framework for reconstructing the history of cosmic energy production. It links resolved galaxy light to the EBL, separates intrinsic and emergent radiation fields, constrains dust processing and AGN energetics, and now extends into the ionising regime relevant for reionisation. In this sense, measuring the CSED as a function of redshift is equivalent to measuring when and how the Universe generated its photons (Driver, 2021).