diff --git a/cosmos/core/airflow.py b/cosmos/core/airflow.py
index 9d3ca90bcd..d869927c28 100644
--- a/cosmos/core/airflow.py
+++ b/cosmos/core/airflow.py
@@ -1,12 +1,12 @@
 import importlib
-from datetime import datetime
 import logging
-from typing import Any, Optional
+from typing import Any, Dict, Optional
 
 from airflow.models import BaseOperator
 from airflow.models.dag import DAG
 from airflow.utils.task_group import TaskGroup
-from cosmos.core.graph.entities import CosmosEntity, Group, Task
+
+from cosmos.core.graph.entities import Group, Task
 
 logger = logging.getLogger(__name__)
 
@@ -28,7 +28,7 @@ def __init__(
 
         super().__init__(*args, **kwargs)
 
-        entities: dict[str, Any] = {}
+        entities: Dict[str, Any] = {}
 
         # render all the entities in the group
         for ent in cosmos_group.entities:
@@ -63,7 +63,7 @@ def __init__(
         kwargs["dag"] = dag
         super().__init__(*args, **kwargs)
 
-        entities: dict[str, Any] = {}
+        entities: Dict[str, Any] = {}
 
         # render all the entities in the group
         for ent in cosmos_group.entities:
diff --git a/cosmos/core/graph/entities.py b/cosmos/core/graph/entities.py
index 05e7351da9..0ef70060ac 100644
--- a/cosmos/core/graph/entities.py
+++ b/cosmos/core/graph/entities.py
@@ -1,9 +1,8 @@
 from __future__ import annotations
 
-from dataclasses import dataclass, field
-from typing import List, Any
-
 import logging
+from dataclasses import dataclass, field
+from typing import Any, Dict, List
 
 logger = logging.getLogger(__name__)
 
@@ -18,7 +17,7 @@ class CosmosEntity:
     """
 
     id: str
-    upstream_entity_ids: list[str] = field(default_factory=list)
+    upstream_entity_ids: List[str] = field(default_factory=list)
 
     def add_upstream(self, entity: CosmosEntity) -> None:
         """
@@ -35,7 +34,7 @@ class Group(CosmosEntity):
     A Group represents a collection of entities that are connected by dependencies.
     """
 
-    entities: list[CosmosEntity] = field(default_factory=list)
+    entities: List[CosmosEntity] = field(default_factory=list)
 
     def add_entity(self, entity: CosmosEntity) -> None:
         """
@@ -58,4 +57,4 @@ class Task(CosmosEntity):
     """
 
     operator_class: str = "airflow.operators.dummy.DummyOperator"
-    arguments: dict[str, Any] = field(default_factory=dict)
+    arguments: Dict[str, Any] = field(default_factory=dict)
diff --git a/cosmos/providers/dbt/core/operators.py b/cosmos/providers/dbt/core/operators.py
index a47911d95b..ad8bda0d20 100644
--- a/cosmos/providers/dbt/core/operators.py
+++ b/cosmos/providers/dbt/core/operators.py
@@ -1,7 +1,7 @@
 from __future__ import annotations
 
 import os
-from typing import Sequence
+from typing import List, Sequence
 
 import yaml
 from airflow.compat.functools import cached_property
@@ -81,7 +81,7 @@ def __init__(
         self,
         project_dir: str,
         conn_id: str,
-        base_cmd: str | list[str] = None,
+        base_cmd: str | List[str] = None,
         select: str = None,
         exclude: str = None,
         selector: str = None,
@@ -251,7 +251,7 @@ def build_and_run_cmd(self, env: dict, cmd_flags: list = None):
         dbt_cmd.append(profile)
 
         ## set env vars
-        env = env | profile_vars
+        env = {**env, **profile_vars}
         result = self.run_command(cmd=dbt_cmd, env=env)
         return result
 
diff --git a/cosmos/providers/dbt/dag.py b/cosmos/providers/dbt/dag.py
index 7fe47d3c70..df94f9356a 100644
--- a/cosmos/providers/dbt/dag.py
+++ b/cosmos/providers/dbt/dag.py
@@ -1,13 +1,16 @@
 """
 This module contains a function to render a dbt project as an Airflow DAG.
 """
-from typing import Any, Literal
+try:
+    from typing import Literal
+except ImportError:
+    from typing_extensions import Literal
+
+from typing import Any, Dict, List
+
 from cosmos.core.airflow import CosmosDag
-from cosmos.providers.dbt.parser.project import DbtProject
-from .render import render_project
 
-from airflow.models import DAG
-from airflow.utils.decorators import apply_defaults
+from .render import render_project
 
 
 class DbtDag(CosmosDag):
@@ -29,11 +32,11 @@ def __init__(
         self,
         dbt_project_name: str,
         conn_id: str,
-        dbt_args: dict[str, Any] = {},
+        dbt_args: Dict[str, Any] = {},
         emit_datasets: bool = True,
         dbt_root_path: str = "/usr/local/airflow/dbt",
         test_behavior: Literal["none", "after_each", "after_all"] = "after_each",
-        dbt_tags: list[str] = [],
+        dbt_tags: List[str] = [],
         *args: Any,
         **kwargs: Any,
     ) -> None:
diff --git a/cosmos/providers/dbt/parser/project.py b/cosmos/providers/dbt/parser/project.py
index 7b00d3c49e..877954bad6 100644
--- a/cosmos/providers/dbt/parser/project.py
+++ b/cosmos/providers/dbt/parser/project.py
@@ -3,14 +3,14 @@
 """
 from __future__ import annotations
 
-import os
 import logging
-import yaml  # type: ignore
-import jinja2
-
+import os
 from dataclasses import dataclass, field
-from typing import Any, ClassVar
 from pathlib import Path
+from typing import Dict
+
+import jinja2
+import yaml  # type: ignore
 
 logger = logging.getLogger(__name__)
 
@@ -116,7 +116,7 @@ class DbtProject:
     dbt_root_path: str = "/usr/local/airflow/dbt"
 
     # private instance variables for managing state
-    models: dict[str, DbtModel] = field(default_factory=dict)
+    models: Dict[str, DbtModel] = field(default_factory=dict)
     project_dir: Path = field(init=False)
     models_dir: Path = field(init=False)
 
@@ -167,7 +167,7 @@ def _handle_config_file(self, path: Path) -> None:
             model_name = config.get("name")
 
             # if the model doesn't exist, we can't do anything
-            if not model_name in self.models:
+            if model_name not in self.models:
                 continue
 
             # parse out the config fields we can recognize
diff --git a/cosmos/providers/dbt/render.py b/cosmos/providers/dbt/render.py
index a5b3334d13..14e76c10af 100644
--- a/cosmos/providers/dbt/render.py
+++ b/cosmos/providers/dbt/render.py
@@ -2,7 +2,13 @@
 This module contains a function to render a dbt project into Cosmos entities.
 """
 import logging
-from typing import Any, Literal
+
+try:
+    from typing import Literal
+except ImportError:
+    from typing_extensions import Literal
+
+from typing import Any, Dict, List
 
 from airflow.datasets import Dataset
 
@@ -15,11 +21,11 @@
 def render_project(
     dbt_project_name: str,
     dbt_root_path: str = "/usr/local/airflow/dbt",
-    task_args: dict[str, Any] = {},
+    task_args: Dict[str, Any] = {},
     test_behavior: Literal["none", "after_each", "after_all"] = "after_each",
     emit_datasets: bool = True,
     conn_id: str = "default_conn_id",
-    dbt_tags: list[str] = [],
+    dbt_tags: List[str] = [],
 ) -> Group:
     """
     Turn a dbt project into a Group
@@ -40,7 +46,7 @@ def render_project(
     )
 
     base_group = Group(id=dbt_project_name)  # this is the group that will be returned
-    entities: dict[
+    entities: Dict[
         str, CosmosEntity
     ] = {}  # this is a dict of all the entities we create
 
@@ -53,8 +59,8 @@ def render_project(
         if dbt_tags and not set(dbt_tags).intersection(model.config.tags):
             continue
 
-        run_args: dict[str, Any] = {**task_args, "models": model_name}
-        test_args: dict[str, Any] = {**task_args, "models": model_name}
+        run_args: Dict[str, Any] = {**task_args, "models": model_name}
+        test_args: Dict[str, Any] = {**task_args, "models": model_name}
 
         if emit_datasets:
             outlets = [
diff --git a/cosmos/providers/dbt/task_group.py b/cosmos/providers/dbt/task_group.py
index 4924558852..14a4f6ad7d 100644
--- a/cosmos/providers/dbt/task_group.py
+++ b/cosmos/providers/dbt/task_group.py
@@ -1,13 +1,16 @@
 """
 This module contains a function to render a dbt project as an Airflow Task Group.
 """
-from typing import Any, Literal
+try:
+    from typing import Literal
+except ImportError:
+    from typing_extensions import Literal
+
+from typing import Any, Dict, List
+
 from cosmos.core.airflow import CosmosTaskGroup
-from cosmos.providers.dbt.parser.project import DbtProject
-from .render import render_project
 
-from airflow.models import DAG
-from airflow.utils.decorators import apply_defaults
+from .render import render_project
 
 
 class DbtTaskGroup(CosmosTaskGroup):
@@ -29,11 +32,11 @@ def __init__(
         self,
         dbt_project_name: str,
         conn_id: str,
-        dbt_args: dict[str, Any] = {},
+        dbt_args: Dict[str, Any] = {},
         emit_datasets: bool = True,
         dbt_root_path: str = "/usr/local/airflow/dbt",
         test_behavior: Literal["none", "after_each", "after_all"] = "after_each",
-        dbt_tags: list[str] = [],
+        dbt_tags: List[str] = [],
         *args: Any,
         **kwargs: Any,
     ) -> None:
diff --git a/pyproject.toml b/pyproject.toml
index f9ebebee9e..38f4b5e4e4 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -37,6 +37,7 @@ classifiers = [
 dependencies = [
     "apache-airflow>=2.4",
     "Jinja2>=3.0.0",
+    "typing-extensions; python_version < '3.8'",
 ]
 
 [project.optional-dependencies]